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Simplifying 180x2 + -1129800x + 952556000 = 0 Reorder the terms: 952556000 + -1129800x + 180x2 = 0 Solving 952556000 + -1129800x + 180x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(47627800 + -56490x + 9x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(47627800 + -56490x + 9x2)' equal to zero and attempt to solve: Simplifying 47627800 + -56490x + 9x2 = 0 Solving 47627800 + -56490x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5291977.778 + -6276.666667x + x2 = 0 Move the constant term to the right: Add '-5291977.778' to each side of the equation. 5291977.778 + -6276.666667x + -5291977.778 + x2 = 0 + -5291977.778 Reorder the terms: 5291977.778 + -5291977.778 + -6276.666667x + x2 = 0 + -5291977.778 Combine like terms: 5291977.778 + -5291977.778 = 0.000 0.000 + -6276.666667x + x2 = 0 + -5291977.778 -6276.666667x + x2 = 0 + -5291977.778 Combine like terms: 0 + -5291977.778 = -5291977.778 -6276.666667x + x2 = -5291977.778 The x term is -6276.666667x. Take half its coefficient (-3138.333334). Square it (9849136.115) and add it to both sides. Add '9849136.115' to each side of the equation. -6276.666667x + 9849136.115 + x2 = -5291977.778 + 9849136.115 Reorder the terms: 9849136.115 + -6276.666667x + x2 = -5291977.778 + 9849136.115 Combine like terms: -5291977.778 + 9849136.115 = 4557158.337 9849136.115 + -6276.666667x + x2 = 4557158.337 Factor a perfect square on the left side: (x + -3138.333334)(x + -3138.333334) = 4557158.337 Calculate the square root of the right side: 2134.750181403 Break this problem into two subproblems by setting (x + -3138.333334) equal to 2134.750181403 and -2134.750181403.Subproblem 1
x + -3138.333334 = 2134.750181403 Simplifying x + -3138.333334 = 2134.750181403 Reorder the terms: -3138.333334 + x = 2134.750181403 Solving -3138.333334 + x = 2134.750181403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3138.333334' to each side of the equation. -3138.333334 + 3138.333334 + x = 2134.750181403 + 3138.333334 Combine like terms: -3138.333334 + 3138.333334 = 0.000000 0.000000 + x = 2134.750181403 + 3138.333334 x = 2134.750181403 + 3138.333334 Combine like terms: 2134.750181403 + 3138.333334 = 5273.083515403 x = 5273.083515403 Simplifying x = 5273.083515403Subproblem 2
x + -3138.333334 = -2134.750181403 Simplifying x + -3138.333334 = -2134.750181403 Reorder the terms: -3138.333334 + x = -2134.750181403 Solving -3138.333334 + x = -2134.750181403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3138.333334' to each side of the equation. -3138.333334 + 3138.333334 + x = -2134.750181403 + 3138.333334 Combine like terms: -3138.333334 + 3138.333334 = 0.000000 0.000000 + x = -2134.750181403 + 3138.333334 x = -2134.750181403 + 3138.333334 Combine like terms: -2134.750181403 + 3138.333334 = 1003.583152597 x = 1003.583152597 Simplifying x = 1003.583152597Solution
The solution to the problem is based on the solutions from the subproblems. x = {5273.083515403, 1003.583152597}Solution
x = {5273.083515403, 1003.583152597}
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