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Created on: 2012-04-11

A sample problem solved by Quickmath web algebra solver

the way to simplify a sum containing 3 terms. (x+2)*(2*x-1) | result of finding solution to an inequality 6*x-2 > 5*x-7

Command

Solve

Equation
6^(8*x) = 216

  1. an equation LHS is equal to a power. The base is six. The exponent is a product that contains 2 factors. The 1st factor of the product is equal to eight. The 2nd factor of the product is x RHS is two hundred and sixteen.
  2. six raised to the power eight times x is equal to two hundred and sixteen;
Variable
Result

Exact

Solution 1 ( complex )
x = log(216^(1/8)*%i/sqrt(2)+216^(1/8)/sqrt(2))/log(6)

  1. an equation Left side of the equation is equal to x Right side of the equation is equal to a rational expression: the top of the rational expression is log of a sum that consists of 2 terms. The 1st term of the sum is a fraction: the top of the fraction is a product that comprises 2 factors. The 1st factor of the product is equal to a power. The base is two hundred and sixteen. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is eight. The 2nd factor of the product is i. The bottom of the fraction is square root of two. The 2nd term of the sum is equal to a quotient: dividend of the quotient is a power. The base is two hundred and sixteen. The exponent is a fraction: the numerator of the fraction is one. The denominator of the fraction is eight. Divisor of the quotient is square root of two. The bottom of the rational expression is logarithm of six.
  2. x is equal to logarithm of two hundred and sixteen raised to the power of one divided by eight times i divided by square root of two plus two hundred and sixteen to the power of one fraction line eight over square root of two divided by logarithm of six;
Solution 2 ( complex )
x = log(216^(1/8)*%i)/log(6)

  1. an equation LHS is equal to x Right side of the equation is equal to a fraction: the numerator of the fraction is log of a product that comprises 2 factors; the 1st factor of the product is equal to a power; the base is two hundred and sixteen; the exponent is a rational expression: the numerator of the rational expression is one; the denominator of the rational expression is eight; the 2nd factor of the product is equal to i; the denominator of the fraction is log of six;
  2. x is equal to logarithm of two hundred and sixteen exponentiated by one divided by eight multiplied by i divided by logarithm of six.
Solution 3 ( complex )
x = log(216^(1/8)*%i/sqrt(2)-216^(1/8)/sqrt(2))/log(6)

  1. an equation Left side of the equation is x Right side of the equation is a fraction: the top of the fraction is log of a sum consisting of 2 terms. The 1st term of the sum is a quotient: dividend of the quotient is a product containing 2 factors. The 1st factor of the product is equal to a power. The base is two hundred and sixteen. The exponent is a fraction: the top of the fraction is one. The bottom of the fraction is eight. The 2nd factor of the product is i. Divisor of the quotient is square root of two. The 2nd term of the sum is equal to a negative fraction: the numerator of the fraction is a power. The base is two hundred and sixteen. The exponent is a fraction: the numerator of the fraction is one. The denominator of the fraction is eight. The denominator of the fraction is square root of two. The bottom of the fraction is log of six.
  2. x is equal to logarithm of two hundred and sixteen to the power of one divided by eight multiplied by i divided by square root of two plus negative two hundred and sixteen to the power one over eight divided by square root of two fraction line logarithm of six.
Solution 4 ( real )
x = log(-216^(1/8))/log(6)

  1. an equation Left side of the equation is equal to x RHS is equal to a fraction: the top of the fraction is logarithm of a negative power; the base is two hundred and sixteen; the exponent is a fraction: the top of the fraction is one; the bottom of the fraction is eight; the bottom of the fraction is log of six;
  2. x is equal to logarithm of negative two hundred and sixteen to the power of one divided by eight fraction line logarithm of six;
Solution 5 ( complex )
x = log(-216^(1/8)*%i/sqrt(2)-216^(1/8)/sqrt(2))/log(6)

  1. an equation LHS is x Right side of the equation is a fraction: the numerator of the fraction is log of 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 a negative power; the base is two hundred and sixteen; the exponent is a fraction: the numerator of the fraction is one; the denominator of the fraction is eight; the 2nd factor of the product is equal to i; the bottom of the fraction is square root of two; the 2nd term of the sum is equal to a negative rational expression: the numerator of the rational expression is a power; the base is two hundred and sixteen; the exponent is a rational expression: the top of the rational expression is one; the bottom of the rational expression is eight; the denominator of the rational expression is square root of two; the denominator of the fraction is logarithm of six;
  2. x is equal to logarithm of negative two hundred and sixteen raised to the power one over eight multiplied by i fraction line square root of two plus negative two hundred and sixteen raised to the power one divided by eight fraction line square root of two divided by logarithm of six;
Solution 6 ( complex )
x = log(-216^(1/8)*%i)/log(6)

  1. an equation LHS is x Right side of the equation is equal to a rational expression: the numerator of the rational expression is logarithm of a product of 2 factors; the 1st factor of the product is equal to a negative power; the base is two hundred and sixteen; the exponent is a fraction: the numerator of the fraction is one; the denominator of the fraction is eight; the 2nd factor of the product is i; the denominator of the rational expression is logarithm of six;
  2. x is equal to logarithm of negative two hundred and sixteen raised to the power one fraction line eight times i fraction line logarithm of six.
Solution 7 ( complex )
x = log(216^(1/8)/sqrt(2)-216^(1/8)*%i/sqrt(2))/log(6)

  1. an equation Left side of the equation is equal to x Right side of the equation is a quotient: dividend of the quotient is logarithm of a sum that contains 2 terms; the 1st term of the sum is equal to a fraction: the top of the fraction is a power; the base is two hundred and sixteen; the exponent is a fraction: the top of the fraction is one; the bottom of the fraction is eight; the bottom of the fraction is square root of two; the 2nd term of the sum is equal to a negative fraction: the numerator of the fraction is a product consisting of 2 factors; the 1st factor of the product is equal to a power; the base is two hundred and sixteen; the exponent is a quotient: dividend of the quotient is one; divisor of the quotient is eight; the 2nd factor of the product is i; the denominator of the fraction is square root of two; divisor of the quotient is log of six;
  2. x is equal to logarithm of two hundred and sixteen exponentiated by one divided by eight over square root of two plus negative two hundred and sixteen raised to the power one fraction line eight multiplied by i over square root of two fraction line logarithm of six;
Solution 8 ( real )
x = log(216)/(8*log(6))

  1. an equation LHS is x RHS is a quotient: dividend of the quotient is logarithm of two hundred and sixteen; divisor of the quotient is a product of 2 factors; the 1st factor of the product is equal to eight; the 2nd factor of the product is equal to logarithm of six;
  2. x is equal to logarithm of two hundred and sixteen divided by eight multiplied by logarithm of six;


Approximate

Solution 1 ( complex )
x = .558111*(.785398*%i+0.67191)

  1. an equation LHS is equal to x Right side of the equation is equal to a product consisting of 2 factors. The 1st factor of the product is equal to zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth. The 2nd factor of the product is equal to a sum consisting of 2 terms. The 1st term of the sum is equal to a product of 2 factors. The 1st factor of the product is equal to zero point seven tenth, eight hundredth, five ten hundredth, three thousandth, nine ten thousandth and eight hundred thousandth. The 2nd factor of the product is equal to i. The 2nd term of the sum is zero point six seven one nine one.
  2. x is zero point five five eight one one one times left brace zero point seven tenth, eight hundredth, five ten hundredth, three thousandth, nine ten thousandth and eight hundred thousandth times i plus zero point six seven one nine one right brace;
Solution 2 ( complex )
x = .558111*(1.5708*%i+0.67191)

  1. an equation LHS is equal to x RHS is equal to a product containing 2 factors; the 1st factor of the product is equal to zero point five five eight one one one; the 2nd factor of the product is equal to a sum containing 2 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 one point five tenth, seven hundredth and eight thousandth; the 2nd factor of the product is i; the 2nd term of the sum is equal to zero point six seven one nine one;
  2. x is zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth times open brace one point five tenth, seven hundredth and eight thousandth times i plus zero point six tenth, seven hundredth, one ten hundredth, nine thousandth and one ten thousandth close brace;
Solution 3 ( complex )
x = .558111*(2.35619*%i+0.67191)

  1. an equation Left side of the equation is equal to x Right side of the equation is equal to a product that comprises 2 factors; the 1st factor of the product is equal to zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth; the 2nd factor of the product is equal to a sum that consists of 2 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 two point three tenth, five hundredth, six ten hundredth, one thousandth and nine ten thousandth; the 2nd factor of the product is equal to i; the 2nd term of the sum is zero point six seven one nine one;
  2. x is zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth times open brace two point three tenth, five hundredth, six ten hundredth, one thousandth and nine ten thousandth times i plus zero point six seven one nine one close brace;
Solution 4 ( complex )
x = .558111*(3.14159*%i+0.67191)

  1. an equation LHS is equal to x Right side of the equation is equal to a product that consists of 2 factors. The 1st factor of the product is equal to zero point five five eight one one one. The 2nd factor of the product is a sum that comprises 2 terms. The 1st term of the sum is equal to a product of 2 factors. The 1st factor of the product is equal to three point one four one five nine. The 2nd factor of the product is i. The 2nd term of the sum is equal to zero point six seven one nine one.
  2. x is zero point five five eight one one one multiplied by open parenthesis three point one tenth, four hundredth, one ten hundredth, five thousandth and nine ten thousandth multiplied by i plus zero point six seven one nine one close parenthesis;
Solution 5 ( complex )
x = .558111*(0.67191-2.35619*%i)

  1. an equation Left side of the equation is equal to x RHS is a product that contains 2 factors; the 1st factor of the product is zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth; the 2nd factor of the product is equal to a sum that contains 2 terms; the 1st term of the sum is equal to zero point six seven one nine one; the 2nd term of the sum is equal to a negative product containing 2 factors; the 1st factor of the product is equal to two point three tenth, five hundredth, six ten hundredth, one thousandth and nine ten thousandth; the 2nd factor of the product is equal to i;
  2. x is equal to zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth multiplied by opening parenthesis zero point six seven one nine one plus negative two point three five six one nine multiplied by i closing parenthesis.
Solution 6 ( complex )
x = .558111*(0.67191-1.5708*%i)

  1. an equation LHS is equal to x RHS is a product comprising 2 factors; the 1st factor of the product is equal to zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth; the 2nd factor of the product is equal to a sum of 2 terms; the 1st term of the sum is equal to zero point six seven one nine one; 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 one point five seven zero eight; the 2nd factor of the product is equal to i;
  2. x is equal to zero point five five eight one one one times left brace zero point six seven one nine one plus negative one point five seven zero eight multiplied by i right brace.
Solution 7 ( complex )
x = .558111*(0.67191-.785398*%i)

  1. an equation LHS is equal to x RHS is equal to a product consisting of 2 factors; the 1st factor of the product is equal to zero point five tenth, five hundredth, eight ten hundredth, one thousandth, one ten thousandth and one hundred thousandth; the 2nd factor of the product is equal to a sum that comprises 2 terms; the 1st term of the sum is zero point six tenth, seven hundredth, one ten hundredth, nine thousandth and one ten thousandth; the 2nd term of the sum is equal to a negative product containing 2 factors; the 1st factor of the product is zero point seven eight five three nine eight; the 2nd factor of the product is equal to i;
  2. x is zero point five five eight one one one multiplied by left bracket zero point six tenth, seven hundredth, one ten hundredth, nine thousandth and one ten thousandth plus negative zero point seven tenth, eight hundredth, five ten hundredth, three thousandth, nine ten thousandth and eight hundred thousandth multiplied by i right bracket.
Solution 8 ( real )
x = 0.375

  1. an equation Left side of the equation is x RHS is equal to zero point three tenth, seven hundredth and five ten hundredth;
  2. x is equal to zero point three seven five;