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Created on: 2012-03-11

A sample problem solved by Quickmath online algebra solver

study easy methods to multiply out a sum that consists of 3 terms; | (5*p-4)/6-(2*p+3)/2 = 7 equation solved

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Equation
1/4*x^4-1/2*x^3+(-11)/4*x^2+7/2*x+8 = 0

  1. an equation Left side of the equation is equal to a sum comprising 5 terms; the 1st term of the sum is equal to a product that contains 2 factors; the 1st factor of the product is equal to a fraction: the top of the fraction is one; the bottom of the fraction is four; the 2nd factor of the product is equal to a power; the base is x; the exponent is four; the 2nd term of the sum is equal to a negative product containing 2 factors; the 1st factor of the product is a fraction: the top of the fraction is one; the bottom of the fraction is two; the 2nd factor of the product is equal to a power; the base is x; the exponent is three; the 3rd term of the sum is equal to a product containing 2 factors; the 1st factor of the product is equal to a fraction: the top of the fraction is negative eleven; the bottom of the fraction is four; the 2nd factor of the product is a power; the base is x; the exponent is two; the 4th term of the sum is equal to a product consisting of 2 factors; the 1st factor of the product is equal to a rational expression: the top of the rational expression is seven; the bottom of the rational expression is two; the 2nd factor of the product is equal to x; the 5th term of the sum is equal to eight Right side of the equation is equal to zero;
  2. one over four times x to the power of four plus negative one divided by two times x to the power of three plus negative eleven fraction line four multiplied by x raised to the power of two plus seven divided by two multiplied by x plus eight is equal to zero;
Variable
Result

Exact

Solution 1 ( real )
x = -sqrt(12*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6)/sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)-(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)-589/(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3))+50/3)/2-sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)/(6*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6))+1/2

  1. an equation LHS is equal to x Right side of the equation is equal to a sum of 3 terms. The 1st term of the sum is equal to a fraction: the top of the fraction is negative square root of a sum that comprises 4 terms. The 1st term of the sum is equal to a rational expression: the numerator of the rational expression is a product comprising 2 factors. The 1st factor of the product is twelve. The 2nd factor of the product is equal to a power. The base is a sum that contains 2 terms. The 1st term of the sum is equal to a rational expression: the numerator of the rational expression is a product that consists of 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The denominator of the rational expression is a power. The base is three. The exponent is a rational expression: the top of the rational expression is three. The bottom of the rational expression is two. The 2nd term of the sum is equal to a fraction: the numerator of the fraction is fourteen thousand and three hundred and twenty nine. The denominator of the fraction is twenty seven. The exponent is a quotient: dividend of the quotient is one. Divisor of the quotient is six. The denominator of the rational expression is square root of a sum consisting of 3 terms. The 1st term of the sum is a product that contains 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is equal to a power. The base is a sum containing 2 terms. The 1st term of the sum is equal to a fraction: the top of the fraction is a product comprising 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a fraction: the top of the fraction is fourteen thousand and three hundred and twenty nine. The bottom of the fraction is twenty seven. The exponent is a rational expression: the top of the rational expression is two. The bottom of the rational expression is three. The 2nd term of the sum is equal to a product of 2 factors. The 1st factor of the product is seventy five. The 2nd factor of the product is equal to a power. The base is a sum that comprises 2 terms. The 1st term of the sum is a fraction: the top of the fraction is a product that consists of 2 factors. The 1st factor of the product is two. The 2nd factor of the product is square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a rational expression: the numerator of the rational expression is three. The denominator of the rational expression is two. The 2nd term of the sum is equal to a rational expression: the numerator of the rational expression is fourteen thousand and three hundred and twenty nine. The denominator of the rational expression is twenty seven. The exponent is a fraction: the numerator of the fraction is one. The denominator of the fraction is three. The 3rd term of the sum is equal to five hundred and eighty nine. The 2nd term of the sum is a negative power. The base is a sum comprising 2 terms. The 1st term of the sum is equal to a rational expression: the top of the rational expression is a product that consists of 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the rational expression is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is three. The 3rd term of the sum is equal to a negative rational expression: the numerator of the rational expression is five hundred and eighty nine. The denominator of the rational expression is a product that consists of 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is a power. The base is a sum of 2 terms. The 1st term of the sum is equal to a fraction: the numerator of the fraction is a product containing 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The denominator of the fraction is a power. The base is three. The exponent is a rational expression: the top of the rational expression is three. The bottom of the rational expression is two. The 2nd term of the sum is equal to a quotient: dividend of the quotient is fourteen thousand and three hundred and twenty nine. Divisor of the quotient is twenty seven. The exponent is a fraction: the top of the fraction is one. The bottom of the fraction is three. The 4th term of the sum is a rational expression: the numerator of the rational expression is fifty. The denominator of the rational expression is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a negative fraction: the numerator of the fraction is square root of a sum of 3 terms. The 1st term of the sum is equal to a product that consists of 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is equal to a power. The base is a sum of 2 terms. The 1st term of the sum is a rational expression: the numerator of the rational expression is a product of 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is square root of nine thousand and one hundred nine. The denominator of the rational expression is a power. The base is three. The exponent is a rational expression: the numerator of the rational expression is three. The denominator of the rational expression is two. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a fraction: the top of the fraction is two. The bottom of the fraction is three. The 2nd term of the sum is equal to a product that contains 2 factors. The 1st factor of the product is seventy five. The 2nd factor of the product is equal to a power. The base is a sum that contains 2 terms. The 1st term of the sum is a rational expression: the top of the rational expression is a product comprising 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the rational expression is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a quotient: dividend of the quotient is one. Divisor of the quotient is three. The 3rd term of the sum is five hundred and eighty nine. The denominator of the fraction is a product that consists of 2 factors. The 1st factor of the product is equal to six. The 2nd factor of the product is a power. The base is a sum comprising 2 terms. The 1st term of the sum is equal to a fraction: the top of the fraction is a product that consists of 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a rational expression: the numerator of the rational expression is fourteen thousand and three hundred and twenty nine. The denominator of the rational expression is twenty seven. The exponent is a quotient: dividend of the quotient is one. Divisor of the quotient is six. The 3rd term of the sum is equal to a fraction: the numerator of the fraction is one. The denominator of the fraction is two.
  2. x is equal to negative square root of twelve multiplied by open bracket two multiplied by square root of nine thousand and one hundred nine fraction line three exponentiated by three divided by two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven close bracket raised to the power one divided by six over square root of nine multiplied by left parenthesis two times square root of nine thousand and one hundred nine fraction line three to the power of three over two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven right parenthesis to the power of two divided by three plus seventy five multiplied by opening bracket two multiplied by square root of nine thousand and one hundred nine fraction line three to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine over twenty seven closing bracket exponentiated by one fraction line three plus five hundred and eighty nine plus negative open bracket two multiplied by square root of nine thousand and one hundred nine fraction line three to the power of three over two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven close bracket to the power of one over three plus negative five hundred and eighty nine fraction line nine times opening parenthesis two multiplied by square root of nine thousand and one hundred nine divided by three to the power three over two plus fourteen thousand and three hundred and twenty nine over twenty seven closing parenthesis raised to the power one divided by three plus fifty divided by three divided by two plus negative square root of nine multiplied by opening brace two times square root of nine thousand and one hundred nine fraction line three raised to the power three fraction line two plus fourteen thousand and three hundred and twenty nine over twenty seven closing brace exponentiated by two divided by three plus seventy five multiplied by opening parenthesis two times square root of nine thousand and one hundred nine divided by three raised to the power of three over two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven closing parenthesis exponentiated by one fraction line three plus five hundred and eighty nine over six multiplied by left bracket two multiplied by square root of nine thousand and one hundred nine divided by three to the power three over two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven right bracket to the power one divided by six plus one fraction line two;
Solution 2 ( real )
x = sqrt(12*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6)/sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)-(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)-589/(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3))+50/3)/2-sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)/(6*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6))+1/2

  1. an equation Left side of the equation is equal to x Right side of the equation is equal to a sum containing 3 terms. The 1st term of the sum is equal to a rational expression: the top of the rational expression is square root of a sum of 4 terms. The 1st term of the sum is equal to a fraction: the numerator of the fraction is a product comprising 2 factors. The 1st factor of the product is equal to twelve. The 2nd factor of the product is equal to a power. The base is a sum that comprises 2 terms. The 1st term of the sum is a fraction: the top of the fraction is a product that contains 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a fraction: the numerator of the fraction is three. The denominator of the fraction is two. The 2nd term of the sum is equal to a fraction: the numerator of the fraction is fourteen thousand and three hundred and twenty nine. The denominator of the fraction is twenty seven. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is six. The denominator of the fraction is square root of a sum that comprises 3 terms. The 1st term of the sum is a product that comprises 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is equal to a power. The base is a sum that comprises 2 terms. The 1st term of the sum is equal to a fraction: the top of the fraction is a product that comprises 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a quotient: dividend of the quotient is fourteen thousand and three hundred and twenty nine. Divisor of the quotient is twenty seven. The exponent is a fraction: the top of the fraction is two. The bottom of the fraction is three. The 2nd term of the sum is a product that comprises 2 factors. The 1st factor of the product is seventy five. The 2nd factor of the product is equal to a power. The base is a sum consisting of 2 terms. The 1st term of the sum is equal to a rational expression: the numerator of the rational expression is a product that comprises 2 factors. The 1st factor of the product is two. The 2nd factor of the product is square root of nine thousand and one hundred nine. The denominator of the rational expression is a power. The base is three. The exponent is a fraction: the numerator of the fraction is three. The denominator of the fraction is two. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a rational expression: the numerator of the rational expression is one. The denominator of the rational expression is three. The 3rd term of the sum is equal to five hundred and eighty nine. The 2nd term of the sum is a negative power. The base is a sum consisting of 2 terms. The 1st term of the sum is a fraction: the top of the fraction is a product that consists of 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a rational expression: the numerator of the rational expression is three. The denominator of the rational expression is two. The 2nd term of the sum is equal to a quotient: dividend of the quotient is fourteen thousand and three hundred and twenty nine. Divisor of the quotient is twenty seven. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is three. The 3rd term of the sum is equal to a negative rational expression: the top of the rational expression is five hundred and eighty nine. The bottom of the rational expression is a product that consists of 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is a power. The base is a sum that comprises 2 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is a product that comprises 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. Divisor of the quotient is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a fraction: the numerator of the fraction is fourteen thousand and three hundred and twenty nine. The denominator of the fraction is twenty seven. The exponent is a rational expression: the numerator of the rational expression is one. The denominator of the rational expression is three. The 4th term of the sum is equal to a rational expression: the top of the rational expression is fifty. The bottom of the rational expression is three. The bottom of the rational expression is two. The 2nd term of the sum is equal to a negative rational expression: the top of the rational expression is square root of a sum that contains 3 terms. The 1st term of the sum is equal to a product consisting of 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is equal to a power. The base is a sum consisting of 2 terms. The 1st term of the sum is equal to a rational expression: the top of the rational expression is a product that comprises 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the rational expression is a power. The base is three. The exponent is a fraction: the numerator of the fraction is three. The denominator of the fraction is two. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a quotient: dividend of the quotient is two. Divisor of the quotient is three. The 2nd term of the sum is a product that contains 2 factors. The 1st factor of the product is equal to seventy five. The 2nd factor of the product is equal to a power. The base is a sum that contains 2 terms. The 1st term of the sum is equal to a fraction: the numerator of the fraction is a product of 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The denominator of the fraction is a power. The base is three. The exponent is a fraction: the numerator of the fraction is three. The denominator of the fraction is two. The 2nd term of the sum is equal to a fraction: the top of the fraction is fourteen thousand and three hundred and twenty nine. The bottom of the fraction is twenty seven. The exponent is a quotient: dividend of the quotient is one. Divisor of the quotient is three. The 3rd term of the sum is equal to five hundred and eighty nine. The bottom of the rational expression is a product comprising 2 factors. The 1st factor of the product is six. The 2nd factor of the product is a power. The base is a sum that consists of 2 terms. The 1st term of the sum is equal to a fraction: the numerator of the fraction is a product comprising 2 factors. The 1st factor of the product is two. The 2nd factor of the product is square root of nine thousand and one hundred nine. The denominator of the fraction is a power. The base is three. The exponent is a fraction: the numerator of the fraction is three. The denominator of the fraction is two. The 2nd term of the sum is a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a fraction: the top of the fraction is one. The bottom of the fraction is six. The 3rd term of the sum is equal to a rational expression: the top of the rational expression is one. The bottom of the rational expression is two.
  2. x is square root of twelve times opening parenthesis two multiplied by square root of nine thousand and one hundred nine over three to the power three fraction line two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven closing parenthesis to the power of one divided by six divided by square root of nine multiplied by left bracket two multiplied by square root of nine thousand and one hundred nine divided by three raised to the power of three divided by two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven right bracket to the power of two over three plus seventy five multiplied by opening brace two multiplied by square root of nine thousand and one hundred nine fraction line three to the power three divided by two plus fourteen thousand and three hundred and twenty nine divided by twenty seven closing brace raised to the power of one divided by three plus five hundred and eighty nine plus negative open bracket two multiplied by square root of nine thousand and one hundred nine fraction line three raised to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine over twenty seven close bracket to the power one fraction line three plus negative five hundred and eighty nine fraction line nine times open brace two times square root of nine thousand and one hundred nine fraction line three raised to the power three fraction line two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven close brace raised to the power one divided by three plus fifty over three fraction line two plus negative square root of nine multiplied by open bracket two multiplied by square root of nine thousand and one hundred nine divided by three raised to the power of three over two plus fourteen thousand and three hundred and twenty nine over twenty seven close bracket to the power two divided by three plus seventy five times open bracket two multiplied by square root of nine thousand and one hundred nine over three to the power three fraction line two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven close bracket to the power one divided by three plus five hundred and eighty nine over six times left parenthesis two times square root of nine thousand and one hundred nine fraction line three to the power three divided by two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven right parenthesis raised to the power one divided by six plus one fraction line two.
Solution 3 ( real )
x = -sqrt(-12*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6)/sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)-(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)-589/(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3))+50/3)/2+sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)/(6*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6))+1/2

  1. an equation LHS is equal to x RHS is equal to a sum consisting of 3 terms. The 1st term of the sum is equal to a fraction: the top of the fraction is negative square root of a sum that contains 4 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is a product containing 2 factors. The 1st factor of the product is equal to negative twelve. The 2nd factor of the product is equal to a power. The base is a sum that comprises 2 terms. The 1st term of the sum is equal to a rational expression: the top of the rational expression is a product containing 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the rational expression is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is a quotient: dividend of the quotient is fourteen thousand and three hundred and twenty nine. Divisor of the quotient is twenty seven. The exponent is a quotient: dividend of the quotient is one. Divisor of the quotient is six. Divisor of the quotient is square root of a sum that comprises 3 terms. The 1st term of the sum is equal to a product containing 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is a power. The base is a sum that contains 2 terms. The 1st term of the sum is equal to a fraction: the numerator of the fraction is a product consisting of 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The denominator of the fraction is a power. The base is three. The exponent is a rational expression: the numerator of the rational expression is three. The denominator of the rational expression is two. The 2nd term of the sum is equal to a rational expression: the numerator of the rational expression is fourteen thousand and three hundred and twenty nine. The denominator of the rational expression is twenty seven. The exponent is a fraction: the numerator of the fraction is two. The denominator of the fraction is three. The 2nd term of the sum is equal to a product that comprises 2 factors. The 1st factor of the product is equal to seventy five. The 2nd factor of the product is equal to a power. The base is a sum consisting of 2 terms. The 1st term of the sum is a rational expression: the numerator of the rational expression is a product of 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The denominator of the rational expression is a power. The base is three. The exponent is a fraction: the numerator of the fraction is three. The denominator of the fraction is two. The 2nd term of the sum is a quotient: dividend of the quotient is fourteen thousand and three hundred and twenty nine. Divisor of the quotient is twenty seven. The exponent is a fraction: the numerator of the fraction is one. The denominator of the fraction is three. The 3rd term of the sum is equal to five hundred and eighty nine. The 2nd term of the sum is a negative power. The base is a sum comprising 2 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is a product comprising 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. Divisor of the quotient is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a rational expression: the numerator of the rational expression is one. The denominator of the rational expression is three. The 3rd term of the sum is equal to a negative rational expression: the numerator of the rational expression is five hundred and eighty nine. The denominator of the rational expression is a product that consists of 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is equal to a power. The base is a sum consisting of 2 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is a product comprising 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. Divisor of the quotient is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a quotient: dividend of the quotient is fourteen thousand and three hundred and twenty nine. Divisor of the quotient is twenty seven. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is three. The 4th term of the sum is equal to a rational expression: the top of the rational expression is fifty. The bottom of the rational expression is three. The bottom of the fraction is two. The 2nd term of the sum is a rational expression: the top of the rational expression is square root of a sum that comprises 3 terms. The 1st term of the sum is equal to a product consisting of 2 factors. The 1st factor of the product is nine. The 2nd factor of the product is equal to a power. The base is a sum that consists of 2 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is a product that contains 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. Divisor of the quotient is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a fraction: the numerator of the fraction is fourteen thousand and three hundred and twenty nine. The denominator of the fraction is twenty seven. The exponent is a fraction: the top of the fraction is two. The bottom of the fraction is three. The 2nd term of the sum is equal to a product comprising 2 factors. The 1st factor of the product is equal to seventy five. The 2nd factor of the product is equal to a power. The base is a sum consisting of 2 terms. The 1st term of the sum is equal to a rational expression: the top of the rational expression is a product that comprises 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is square root of nine thousand and one hundred nine. The bottom of the rational expression is a power. The base is three. The exponent is a rational expression: the top of the rational expression is three. The bottom of the rational expression is two. The 2nd term of the sum is equal to a fraction: the top of the fraction is fourteen thousand and three hundred and twenty nine. The bottom of the fraction is twenty seven. The exponent is a fraction: the numerator of the fraction is one. The denominator of the fraction is three. The 3rd term of the sum is equal to five hundred and eighty nine. The bottom of the rational expression is a product containing 2 factors. The 1st factor of the product is equal to six. The 2nd factor of the product is equal to a power. The base is a sum that comprises 2 terms. The 1st term of the sum is equal to a rational expression: the top of the rational expression is a product that comprises 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the rational expression is a power. The base is three. The exponent is a rational expression: the top of the rational expression is three. The bottom of the rational expression is two. The 2nd term of the sum is equal to a rational expression: the numerator of the rational expression is fourteen thousand and three hundred and twenty nine. The denominator of the rational expression is twenty seven. The exponent is a fraction: the top of the fraction is one. The bottom of the fraction is six. The 3rd term of the sum is a quotient: dividend of the quotient is one. Divisor of the quotient is two.
  2. x is equal to negative square root of negative twelve multiplied by open parenthesis two times square root of nine thousand and one hundred nine over three to the power of three over two plus fourteen thousand and three hundred and twenty nine divided by twenty seven close parenthesis raised to the power of one fraction line six divided by square root of nine multiplied by open parenthesis two multiplied by square root of nine thousand and one hundred nine fraction line three raised to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine divided by twenty seven close parenthesis exponentiated by two over three plus seventy five times open parenthesis two times square root of nine thousand and one hundred nine fraction line three raised to the power three divided by two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven close parenthesis raised to the power of one fraction line three plus five hundred and eighty nine plus negative left brace two multiplied by square root of nine thousand and one hundred nine divided by three raised to the power three over two plus fourteen thousand and three hundred and twenty nine over twenty seven right brace raised to the power one fraction line three plus negative five hundred and eighty nine divided by nine times left parenthesis two times square root of nine thousand and one hundred nine fraction line three raised to the power of three divided by two plus fourteen thousand and three hundred and twenty nine over twenty seven right parenthesis exponentiated by one over three plus fifty divided by three divided by two plus square root of nine multiplied by open bracket two multiplied by square root of nine thousand and one hundred nine fraction line three to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine divided by twenty seven close bracket to the power two divided by three plus seventy five multiplied by left bracket two times square root of nine thousand and one hundred nine fraction line three raised to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine over twenty seven right bracket exponentiated by one divided by three plus five hundred and eighty nine divided by six multiplied by opening bracket two times square root of nine thousand and one hundred nine fraction line three exponentiated by three over two plus fourteen thousand and three hundred and twenty nine over twenty seven closing bracket raised to the power of one over six plus one fraction line two;
Solution 4 ( real )
x = sqrt(-12*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6)/sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)-(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)-589/(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3))+50/3)/2+sqrt(9*(2*sqrt(9109)/3^(3/2)+14329/27)^(2/3)+75*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/3)+589)/(6*(2*sqrt(9109)/3^(3/2)+14329/27)^(1/6))+1/2

  1. an equation Left side of the equation is equal to x Right side of the equation is equal to a sum that comprises 3 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is square root of a sum consisting of 4 terms. The 1st term of the sum is equal to a fraction: the top of the fraction is a product that comprises 2 factors. The 1st factor of the product is negative twelve. The 2nd factor of the product is equal to a power. The base is a sum comprising 2 terms. The 1st term of the sum is a fraction: the top of the fraction is a product containing 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a rational expression: the numerator of the rational expression is three. The denominator of the rational expression is two. The 2nd term of the sum is a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a rational expression: the numerator of the rational expression is one. The denominator of the rational expression is six. The bottom of the fraction is square root of a sum comprising 3 terms. The 1st term of the sum is equal to a product that comprises 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is a power. The base is a sum that consists of 2 terms. The 1st term of the sum is a fraction: the top of the fraction is a product comprising 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The bottom of the fraction is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a fraction: the numerator of the fraction is two. The denominator of the fraction is three. The 2nd term of the sum is a product that contains 2 factors. The 1st factor of the product is seventy five. The 2nd factor of the product is equal to a power. The base is a sum that contains 2 terms. The 1st term of the sum is a rational expression: the numerator of the rational expression is a product of 2 factors. The 1st factor of the product is two. The 2nd factor of the product is square root of nine thousand and one hundred nine. The denominator of the rational expression is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a fraction: the numerator of the fraction is fourteen thousand and three hundred and twenty nine. The denominator of the fraction is twenty seven. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is three. The 3rd term of the sum is equal to five hundred and eighty nine. The 2nd term of the sum is equal to a negative power. The base is a sum containing 2 terms. The 1st term of the sum is a quotient: dividend of the quotient is a product consisting of 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. Divisor of the quotient is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a rational expression: the numerator of the rational expression is fourteen thousand and three hundred and twenty nine. The denominator of the rational expression is twenty seven. The exponent is a fraction: the top of the fraction is one. The bottom of the fraction is three. The 3rd term of the sum is equal to a negative quotient: dividend of the quotient is five hundred and eighty nine. Divisor of the quotient is a product of 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is a power. The base is a sum of 2 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is a product comprising 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. Divisor of the quotient is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a rational expression: the numerator of the rational expression is fourteen thousand and three hundred and twenty nine. The denominator of the rational expression is twenty seven. The exponent is a quotient: dividend of the quotient is one. Divisor of the quotient is three. The 4th term of the sum is equal to a rational expression: the top of the rational expression is fifty. The bottom of the rational expression is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a fraction: the numerator of the fraction is square root of a sum that comprises 3 terms. The 1st term of the sum is equal to a product that comprises 2 factors. The 1st factor of the product is nine. The 2nd factor of the product is a power. The base is a sum containing 2 terms. The 1st term of the sum is equal to a rational expression: the numerator of the rational expression is a product that comprises 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The denominator of the rational expression is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a quotient: dividend of the quotient is fourteen thousand and three hundred and twenty nine. Divisor of the quotient is twenty seven. The exponent is a fraction: the numerator of the fraction is two. The denominator of the fraction is three. The 2nd term of the sum is equal to a product containing 2 factors. The 1st factor of the product is equal to seventy five. The 2nd factor of the product is equal to a power. The base is a sum comprising 2 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is a product that contains 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. Divisor of the quotient is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is fourteen thousand and three hundred and twenty nine. The bottom of the rational expression is twenty seven. The exponent is a rational expression: the numerator of the rational expression is one. The denominator of the rational expression is three. The 3rd term of the sum is equal to five hundred and eighty nine. The denominator of the fraction is a product that comprises 2 factors. The 1st factor of the product is equal to six. The 2nd factor of the product is equal to a power. The base is a sum of 2 terms. The 1st term of the sum is a rational expression: the numerator of the rational expression is a product containing 2 factors. The 1st factor of the product is two. The 2nd factor of the product is equal to square root of nine thousand and one hundred nine. The denominator of the rational expression is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The 2nd term of the sum is equal to a fraction: the numerator of the fraction is fourteen thousand and three hundred and twenty nine. The denominator of the fraction is twenty seven. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is six. The 3rd term of the sum is a fraction: the top of the fraction is one. The bottom of the fraction is two.
  2. x is equal to square root of negative twelve multiplied by open bracket two multiplied by square root of nine thousand and one hundred nine divided by three raised to the power of three divided by two plus fourteen thousand and three hundred and twenty nine divided by twenty seven close bracket raised to the power one fraction line six fraction line square root of nine multiplied by opening bracket two multiplied by square root of nine thousand and one hundred nine fraction line three to the power three divided by two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven closing bracket raised to the power two fraction line three plus seventy five times left parenthesis two times square root of nine thousand and one hundred nine over three exponentiated by three over two plus fourteen thousand and three hundred and twenty nine over twenty seven right parenthesis raised to the power one over three plus five hundred and eighty nine plus negative left parenthesis two times square root of nine thousand and one hundred nine divided by three exponentiated by three divided by two plus fourteen thousand and three hundred and twenty nine over twenty seven right parenthesis raised to the power of one over three plus negative five hundred and eighty nine fraction line nine multiplied by open parenthesis two multiplied by square root of nine thousand and one hundred nine divided by three to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine over twenty seven close parenthesis to the power of one over three plus fifty fraction line three fraction line two plus square root of nine multiplied by open parenthesis two multiplied by square root of nine thousand and one hundred nine fraction line three to the power of three divided by two plus fourteen thousand and three hundred and twenty nine fraction line twenty seven close parenthesis exponentiated by two over three plus seventy five times opening brace two times square root of nine thousand and one hundred nine divided by three to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine over twenty seven closing brace raised to the power of one divided by three plus five hundred and eighty nine divided by six multiplied by opening brace two multiplied by square root of nine thousand and one hundred nine fraction line three raised to the power of three fraction line two plus fourteen thousand and three hundred and twenty nine over twenty seven closing brace to the power of one fraction line six plus one fraction line two.


Approximate

Solution 1 ( real )
x = -2.54377

  1. an equation LHS is equal to x RHS is negative two point five tenth, four hundredth, three ten hundredth, seven thousandth and seven ten thousandth.
  2. x is equal to negative two point five four three seven seven.
Solution 2 ( real )
x = -1.40771

  1. an equation LHS is equal to x Right side of the equation is equal to negative one point four zero seven seven one;
  2. x is equal to negative one point four tenth, seven ten hundredth, seven thousandth and one ten thousandth;
Solution 3 ( complex )
x = 2.97574-.285062*%i

  1. an equation LHS is equal to x RHS is equal to a sum comprising 2 terms; the 1st term of the sum is equal to two point nine seven five seven four; the 2nd term of the sum is equal to a negative product that consists of 2 factors; the 1st factor of the product is equal to zero point two eight five zero six two; the 2nd factor of the product is equal to i;
  2. x is equal to two point nine seven five seven four plus negative zero point two eight five zero six two multiplied by i;
Solution 4 ( complex )
x = .285062*%i+2.97574

  1. an equation LHS is equal to x Right side of the equation is a sum consisting of 2 terms; the 1st term of the sum is a product that contains 2 factors; the 1st factor of the product is equal to zero point two tenth, eight hundredth, five ten hundredth, six ten thousandth and two hundred thousandth; the 2nd factor of the product is i; the 2nd term of the sum is equal to two point nine seven five seven four;
  2. x is equal to zero point two tenth, eight hundredth, five ten hundredth, six ten thousandth and two hundred thousandth times i plus two point nine seven five seven four;