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Created on: 2012-03-30

A sample problem solved by Quickmath math solver

partial fraction decomposition of a fraction;

Command

Solve

Equation
x*(x-7)^3+x*(x-2) = 0

  1. an equation LHS is equal to a sum that consists of 2 terms; the first term of the sum is equal to a product consisting of 2 factors; the first factor of the product is x; the second factor of the product is a power; the base is a sum that comprises 2 terms; the first term of the sum is x; the second term of the sum is equal to negative seven; the exponent is three; the second term of the sum is a product of 2 factors; the first factor of the product is x; the second factor of the product is equal to a sum containing 2 terms; the first term of the sum is x; the second term of the sum is equal to negative two RHS is zero;
  2. x times opening parenthesis x plus negative seven closing parenthesis to the power of three plus x times left bracket x plus negative two right bracket is equal to zero;
Variable
Result

Exact

Solution 1 ( complex )
x = -(sqrt(3)*%i/2-1/2)/(3*(sqrt(679)/(2*3^(3/2))-5/2)^(1/3))+(sqrt(679)/(2*3^(3/2))-5/2)^(1/3)*(-sqrt(3)*%i/2-1/2)+7

  1. an equation LHS is equal to x Right side of the equation is a sum consisting of 3 terms; the first term of the sum is equal to a quotient: dividend of the quotient is a negative sum containing 2 terms; the first term of the sum is equal to a fraction: the top of the fraction is a product consisting of 2 factors; the first factor of the product is square root of three; the second factor of the product is i; the bottom of the fraction is two; the second term of the sum is a negative rational expression: the numerator of the rational expression is one; the denominator of the rational expression is two; divisor of the quotient is a product that consists of 2 factors; the first factor of the product is equal to three; the second factor of the product is equal to a power; the base is a sum comprising 2 terms; the first term of the sum is equal to a rational expression: the numerator of the rational expression is square root of six hundred and seventy nine; the denominator of the rational expression is a product comprising 2 factors; the first factor of the product is equal to two; the second factor of the product is equal to a power; the base is three; the exponent is a quotient: dividend of the quotient is three; divisor of the quotient is two; the second term of the sum is a negative fraction: the numerator of the fraction is five; the denominator of the fraction is two; the exponent is a quotient: dividend of the quotient is one; divisor of the quotient is three; the second term of the sum is a product consisting of 2 factors; the first factor of the product is a power; the base is a sum that comprises 2 terms; the first term of the sum is equal to a fraction: the top of the fraction is square root of six hundred and seventy nine; the bottom of the fraction is a product that consists of 2 factors; the first factor of the product is equal to two; the second factor of the product is equal to a power; the base is three; the exponent is a quotient: dividend of the quotient is three; divisor of the quotient is two; the second term of the sum is equal to a negative rational expression: the top of the rational expression is five; the bottom of the rational expression is two; the exponent is a rational expression: the numerator of the rational expression is one; the denominator of the rational expression is three; the second factor of the product is equal to a sum comprising 2 terms; the first term of the sum is equal to a fraction: the numerator of the fraction is a product that comprises 2 factors; the first factor of the product is negative square root of three; the second factor of the product is equal to i; the denominator of the fraction is two; the second term of the sum is equal to a negative quotient: dividend of the quotient is one; divisor of the quotient is two; the third term of the sum is seven;
  2. x is equal to negative opening parenthesis square root of three multiplied by i divided by two plus negative one over two closing parenthesis fraction line three multiplied by open brace square root of six hundred and seventy nine over two times three raised to the power of three divided by two plus negative five divided by two close brace to the power of one divided by three plus open bracket square root of six hundred and seventy nine divided by two multiplied by three raised to the power three fraction line two plus negative five fraction line two close bracket raised to the power one fraction line three multiplied by left bracket negative square root of three times i over two plus negative one over two right bracket plus seven;
Solution 2 ( complex )
x = (sqrt(679)/(2*3^(3/2))-5/2)^(1/3)*(sqrt(3)*%i/2-1/2)-(-sqrt(3)*%i/2-1/2)/(3*(sqrt(679)/(2*3^(3/2))-5/2)^(1/3))+7

  1. an equation LHS is equal to x Right side of the equation is a sum comprising 3 terms. The first term of the sum is a product that contains 2 factors. The first factor of the product is equal to a power. The base is a sum that consists of 2 terms. The first term of the sum is a rational expression: the top of the rational expression is square root of six hundred and seventy nine. The bottom of the rational expression is a product of 2 factors. The first factor of the product is two. The second factor of the product 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 second term of the sum is a negative fraction: the numerator of the fraction is five. The denominator of the fraction is two. The exponent is a fraction: the top of the fraction is one. The bottom of the fraction is three. The second factor of the product is equal to a sum comprising 2 terms. The first term of the sum is a fraction: the top of the fraction is a product that consists of 2 factors. The first factor of the product is equal to square root of three. The second factor of the product is equal to i. The bottom of the fraction is two. The second term of the sum is a negative rational expression: the numerator of the rational expression is one. The denominator of the rational expression is two. The second term of the sum is a negative rational expression: the top of the rational expression is a sum comprising 2 terms. The first term of the sum is equal to a fraction: the numerator of the fraction is a product that consists of 2 factors. The first factor of the product is negative square root of three. The second factor of the product is i. The denominator of the fraction is two. The second term of the sum is equal to a negative fraction: the numerator of the fraction is one. The denominator of the fraction is two. The bottom of the rational expression is a product that contains 2 factors. The first factor of the product is three. The second factor of the product is equal to a power. The base is a sum comprising 2 terms. The first term of the sum is a quotient: dividend of the quotient is square root of six hundred and seventy nine. Divisor of the quotient is a product containing 2 factors. The first factor of the product is equal to two. The second factor of the product is equal to 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 second term of the sum is equal to a negative fraction: the top of the fraction is five. The bottom of the fraction is two. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is three. The third term of the sum is equal to seven.
  2. x is equal to open brace square root of six hundred and seventy nine fraction line two multiplied by three raised to the power three divided by two plus negative five fraction line two close brace raised to the power of one fraction line three times left brace square root of three multiplied by i divided by two plus negative one divided by two right brace plus negative negative square root of three multiplied by i over two plus negative one divided by two fraction line three times open bracket square root of six hundred and seventy nine divided by two times three raised to the power of three divided by two plus negative five over two close bracket exponentiated by one fraction line three plus seven;
Solution 3 ( real )
x = (sqrt(679)/(2*3^(3/2))-5/2)^(1/3)-1/(3*(sqrt(679)/(2*3^(3/2))-5/2)^(1/3))+7

  1. an equation Left side of the equation is equal to x RHS is equal to a sum of 3 terms; the first term of the sum is equal to a power; the base is a sum comprising 2 terms; the first term of the sum is a rational expression: the top of the rational expression is square root of six hundred and seventy nine; the bottom of the rational expression is a product that comprises 2 factors; the first factor of the product is two; the second factor of the product 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 second term of the sum is equal to a negative fraction: the numerator of the fraction is five; the denominator of the fraction is two; the exponent is a rational expression: the top of the rational expression is one; the bottom of the rational expression is three; the second term of the sum is a negative quotient: dividend of the quotient is one; divisor of the quotient is a product that consists of 2 factors; the first factor of the product is equal to three; the second factor of the product is equal to a power; the base is a sum consisting of 2 terms; the first term of the sum is equal to a rational expression: the top of the rational expression is square root of six hundred and seventy nine; the bottom of the rational expression is a product containing 2 factors; the first factor of the product is equal to two; the second factor of the product 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 second term of the sum is equal to a negative quotient: dividend of the quotient is five; divisor of the quotient is two; the exponent is a rational expression: the numerator of the rational expression is one; the denominator of the rational expression is three; the third term of the sum is equal to seven;
  2. x is open parenthesis square root of six hundred and seventy nine divided by two times three raised to the power three over two plus negative five fraction line two close parenthesis raised to the power of one over three plus negative one over three times open brace square root of six hundred and seventy nine divided by two multiplied by three exponentiated by three fraction line two plus negative five fraction line two close brace raised to the power one fraction line three plus seven;
Solution 4 ( real )
x = 0

  1. an equation LHS is equal to x RHS is zero;
  2. x is equal to zero.


Approximate

Solution 1 ( complex )
x = 7.75799-1.65035*%i

  1. an equation Left side of the equation is equal to x RHS is equal to a sum that comprises 2 terms; the first term of the sum is seven point seven tenth, five hundredth, seven ten hundredth, nine thousandth and nine ten thousandth; the second term of the sum is equal to a negative product consisting of 2 factors; the first factor of the product is equal to one point six tenth, five hundredth, three thousandth and five ten thousandth; the second factor of the product is equal to i;
  2. x is equal to seven point seven five seven nine nine plus negative one point six five zero three five times i.
Solution 2 ( complex )
x = 1.65035*%i+7.75799

  1. an equation LHS is x RHS is equal to a sum that contains 2 terms. The first term of the sum is equal to a product containing 2 factors. The first factor of the product is equal to one point six five zero three five. The second factor of the product is i. The second term of the sum is seven point seven tenth, five hundredth, seven ten hundredth, nine thousandth and nine ten thousandth.
  2. x is equal to one point six five zero three five times i plus seven point seven five seven nine nine.
Solution 3 ( real )
x = 5.48402

  1. an equation Left side of the equation is x RHS is equal to five point four tenth, eight hundredth, four ten hundredth and two ten thousandth;
  2. x is five point four tenth, eight hundredth, four ten hundredth and two ten thousandth.
Solution 4 ( real )
x = 0.0

  1. an equation Left side of the equation is equal to x RHS is zero;
  2. x is equal to zero;