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Simplifying -625 = x2 + 250x Reorder the terms: -625 = 250x + x2 Solving -625 = 250x + x2 Solving for variable 'x'. Reorder the terms: -625 + -250x + -1x2 = 250x + -250x + x2 + -1x2 Combine like terms: 250x + -250x = 0 -625 + -250x + -1x2 = 0 + x2 + -1x2 -625 + -250x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -625 + -250x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(625 + 250x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(625 + 250x + x2)' equal to zero and attempt to solve: Simplifying 625 + 250x + x2 = 0 Solving 625 + 250x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-625' to each side of the equation. 625 + 250x + -625 + x2 = 0 + -625 Reorder the terms: 625 + -625 + 250x + x2 = 0 + -625 Combine like terms: 625 + -625 = 0 0 + 250x + x2 = 0 + -625 250x + x2 = 0 + -625 Combine like terms: 0 + -625 = -625 250x + x2 = -625 The x term is 250x. Take half its coefficient (125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. 250x + 15625 + x2 = -625 + 15625 Reorder the terms: 15625 + 250x + x2 = -625 + 15625 Combine like terms: -625 + 15625 = 15000 15625 + 250x + x2 = 15000 Factor a perfect square on the left side: (x + 125)(x + 125) = 15000 Calculate the square root of the right side: 122.474487139 Break this problem into two subproblems by setting (x + 125) equal to 122.474487139 and -122.474487139.Subproblem 1
x + 125 = 122.474487139 Simplifying x + 125 = 122.474487139 Reorder the terms: 125 + x = 122.474487139 Solving 125 + x = 122.474487139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = 122.474487139 + -125 Combine like terms: 125 + -125 = 0 0 + x = 122.474487139 + -125 x = 122.474487139 + -125 Combine like terms: 122.474487139 + -125 = -2.525512861 x = -2.525512861 Simplifying x = -2.525512861Subproblem 2
x + 125 = -122.474487139 Simplifying x + 125 = -122.474487139 Reorder the terms: 125 + x = -122.474487139 Solving 125 + x = -122.474487139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = -122.474487139 + -125 Combine like terms: 125 + -125 = 0 0 + x = -122.474487139 + -125 x = -122.474487139 + -125 Combine like terms: -122.474487139 + -125 = -247.474487139 x = -247.474487139 Simplifying x = -247.474487139Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.525512861, -247.474487139}Solution
x = {-2.525512861, -247.474487139}
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