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Created on: 2012-02-27

A sample problem solved by Quickmath algebra calculator

Command

Solve

Equation
-x^3+0.0592*x = 6.59093

  1. an equation LHS is a sum that contains 2 terms; the 1st term of the sum is equal to a negative power; the base is x; the exponent is three; the 2nd term of the sum is a product containing 2 factors; the 1st factor of the product is zero point zero five nine two; the 2nd factor of the product is equal to x RHS is equal to six point five tenth, nine hundredth, nine thousandth and three ten thousandth;
  2. negative x exponentiated by three plus zero point five hundredth, nine ten hundredth and two thousandth times x is equal to six point five tenth, nine hundredth, nine thousandth and three ten thousandth;
Variable
Result

Exact

Solution 1 ( complex )
x = 37*(sqrt(3)*%i/2-1/2)/(1875*(37*sqrt(52291838)/(15625*3^(3/2))-6179/1875)^(1/3))+(37*sqrt(52291838)/(15625*3^(3/2))-6179/1875)^(1/3)*(-sqrt(3)*%i/2-1/2)

  1. an equation LHS is equal to x Right side of the equation is a sum that comprises 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 thirty seven; the 2nd factor of the product is equal to a sum containing 2 terms; the 1st term of the sum is a rational expression: the numerator of the rational expression is a product consisting of 2 factors; the 1st factor of the product is equal to square root of three; the 2nd factor of the product is i; the denominator of the rational expression is two; the 2nd term of the sum is equal to a negative fraction: the top of the fraction is one; the bottom of the fraction is two; the denominator of the fraction is a product containing 2 factors; the 1st factor of the product is one thousand eight hundred and 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 rational expression: the numerator of the rational expression is a product consisting of 2 factors; the 1st factor of the product is thirty seven; the 2nd factor of the product is equal to square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight; the denominator of the rational expression is a product consisting of 2 factors; the 1st factor of the product is fifteen thousand and six hundred and twenty five; the 2nd 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 2nd term of the sum is equal to a negative fraction: the top of the fraction is six thousand and one hundred seventy nine; the bottom of the fraction is one thousand eight hundred and seventy five; the exponent is a rational expression: the top of the rational expression is one; the bottom of the rational expression is three; the 2nd term of the sum is a product of 2 factors; the 1st 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 rational expression: the top of the rational expression is a product of 2 factors; the 1st factor of the product is equal to thirty seven; the 2nd factor of the product is equal to square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight; the bottom of the rational expression is a product that contains 2 factors; the 1st factor of the product is fifteen thousand and six hundred and twenty five; the 2nd 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 2nd term of the sum is equal to a negative fraction: the top of the fraction is six thousand and one hundred seventy nine; the bottom of the fraction is one thousand eight hundred and seventy five; the exponent is a fraction: the top of the fraction is one; the bottom of the fraction is three; the 2nd factor of the product is equal to a sum that comprises 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 negative square root of three; the 2nd factor of the product is equal to i; the denominator of the fraction is two; the 2nd term of the sum is equal to a negative quotient: dividend of the quotient is one; divisor of the quotient is two;
  2. x is thirty seven multiplied by open bracket square root of three times i over two plus negative one over two close bracket divided by one thousand eight hundred and seventy five times opening brace thirty seven multiplied by square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight fraction line fifteen thousand and six hundred and twenty five multiplied by three to the power three fraction line two plus negative six thousand and one hundred seventy nine over one thousand eight hundred and seventy five closing brace to the power one fraction line three plus left parenthesis thirty seven times square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight divided by fifteen thousand and six hundred and twenty five multiplied by three exponentiated by three over two plus negative six thousand and one hundred seventy nine divided by one thousand eight hundred and seventy five right parenthesis to the power one divided by three times left brace negative square root of three multiplied by i divided by two plus negative one fraction line two right brace.
Solution 2 ( complex )
x = (37*sqrt(52291838)/(15625*3^(3/2))-6179/1875)^(1/3)*(sqrt(3)*%i/2-1/2)+37*(-sqrt(3)*%i/2-1/2)/(1875*(37*sqrt(52291838)/(15625*3^(3/2))-6179/1875)^(1/3))

  1. an equation Left side of the equation is equal to x Right side of the equation is equal to a sum containing 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 a power; the base is a sum that contains 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 thirty seven; the 2nd factor of the product is square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight; the bottom of the rational expression is a product that contains 2 factors; the 1st factor of the product is equal to fifteen thousand and six hundred and twenty five; the 2nd factor of the product is equal to 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 negative rational expression: the numerator of the rational expression is six thousand and one hundred seventy nine; the denominator of the rational expression is one thousand eight hundred and seventy five; the exponent is a rational expression: the top of the rational expression is one; the bottom of the rational expression is three; the 2nd factor of the product is a sum that consists of 2 terms; the 1st term of the sum is a fraction: the numerator of the fraction is a product comprising 2 factors; the 1st factor of the product is equal to square root of three; the 2nd factor of the product is equal to i; the denominator of the fraction is two; the 2nd term of the sum is equal to a negative fraction: the top of the fraction is one; the bottom of the fraction is two; the 2nd term of the sum is equal to a fraction: the numerator of the fraction is a product that consists of 2 factors; the 1st factor of the product is thirty seven; the 2nd factor of the product is a sum that comprises 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 equal to negative square root of three; the 2nd factor of the product is equal to i; the denominator of the fraction is two; the 2nd term of the sum is a negative fraction: the numerator of the fraction is one; the denominator of the fraction is two; the denominator of the fraction is a product that consists of 2 factors; the 1st factor of the product is one thousand eight hundred and seventy five; 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 equal to a fraction: the numerator of the fraction is a product of 2 factors; the 1st factor of the product is thirty seven; the 2nd factor of the product is square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight; the denominator of the fraction is a product comprising 2 factors; the 1st factor of the product is equal to fifteen thousand and six hundred and twenty five; the 2nd factor of the product is equal to 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 negative quotient: dividend of the quotient is six thousand and one hundred seventy nine; divisor of the quotient is one thousand eight hundred and seventy five; the exponent is a rational expression: the top of the rational expression is one; the bottom of the rational expression is three;
  2. x is left bracket thirty seven multiplied by square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight divided by fifteen thousand and six hundred and twenty five multiplied by three raised to the power three fraction line two plus negative six thousand and one hundred seventy nine over one thousand eight hundred and seventy five right bracket exponentiated by one fraction line three times left parenthesis square root of three times i fraction line two plus negative one fraction line two right parenthesis plus thirty seven multiplied by opening parenthesis negative square root of three multiplied by i over two plus negative one divided by two closing parenthesis over one thousand eight hundred and seventy five times open parenthesis thirty seven multiplied by square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight divided by fifteen thousand and six hundred and twenty five multiplied by three raised to the power three fraction line two plus negative six thousand and one hundred seventy nine divided by one thousand eight hundred and seventy five close parenthesis to the power of one fraction line three;
Solution 3 ( real )
x = (37*sqrt(52291838)/(15625*3^(3/2))-6179/1875)^(1/3)+37/(1875*(37*sqrt(52291838)/(15625*3^(3/2))-6179/1875)^(1/3))

  1. an equation Left side of the equation is x RHS is a sum consisting of 2 terms. The 1st term of the sum is equal to a power. The base is a sum of 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 equal to thirty seven. The 2nd factor of the product is square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight. Divisor of the quotient is a product that consists of 2 factors. The 1st factor of the product is equal to fifteen thousand and six hundred and twenty five. The 2nd 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 2nd term of the sum is equal to a negative rational expression: the top of the rational expression is six thousand and one hundred seventy nine. The bottom of the rational expression is one thousand eight hundred and seventy five. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is three. The 2nd term of the sum is equal to a rational expression: the top of the rational expression is thirty seven. The bottom of the rational expression is a product comprising 2 factors. The 1st factor of the product is equal to one thousand eight hundred and 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 quotient: dividend of the quotient is a product that contains 2 factors. The 1st factor of the product is equal to thirty seven. The 2nd factor of the product is equal to square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight. Divisor of the quotient is a product of 2 factors. The 1st factor of the product is equal to fifteen thousand and six hundred and twenty five. The 2nd factor of the product is equal to 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 negative fraction: the top of the fraction is six thousand and one hundred seventy nine. The bottom of the fraction is one thousand eight hundred and seventy five. The exponent is a rational expression: the top of the rational expression is one. The bottom of the rational expression is three.
  2. x is equal to open brace thirty seven multiplied by square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight divided by fifteen thousand and six hundred and twenty five multiplied by three raised to the power three divided by two plus negative six thousand and one hundred seventy nine fraction line one thousand eight hundred and seventy five close brace to the power of one divided by three plus thirty seven fraction line one thousand eight hundred and seventy five multiplied by opening brace thirty seven multiplied by square root of fifty two million and two hundred and ninety one thousand and eight hundred and thirty eight fraction line fifteen thousand and six hundred and twenty five times three raised to the power of three divided by two plus negative six thousand and one hundred seventy nine divided by one thousand eight hundred and seventy five closing brace to the power one over three.


Approximate

Solution 1 ( complex )
x = .942721-1.61461*%i

  1. an equation Left side of the equation is equal to x Right side of the equation is a sum consisting of 2 terms. The 1st term of the sum is equal to zero point nine four two seven two 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 six one four six one. The 2nd factor of the product is i.
  2. x is zero point nine four two seven two one plus negative one point six one four six one times i.
Solution 2 ( complex )
x = 1.61461*%i+.942721

  1. an equation LHS is x Right side of the equation is a sum that consists of 2 terms. The 1st term of the sum is equal to a product consisting of 2 factors. The 1st factor of the product is one point six tenth, one hundredth, four ten hundredth, six thousandth and one ten thousandth. The 2nd factor of the product is i. The 2nd term of the sum is equal to zero point nine tenth, four hundredth, two ten hundredth, seven thousandth, two ten thousandth and one hundred thousandth.
  2. x is one point six one four six one multiplied by i plus zero point nine four two seven two one.
Solution 3 ( real )
x = -1.88544

  1. an equation LHS is x RHS is equal to negative one point eight tenth, eight hundredth, five ten hundredth, four thousandth and four ten thousandth.
  2. x is equal to negative one point eight tenth, eight hundredth, five ten hundredth, four thousandth and four ten thousandth.