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Simplifying -2x2 + 100x = 1000 Reorder the terms: 100x + -2x2 = 1000 Solving 100x + -2x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 100x + -2x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 100x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-500 + 50x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-500 + 50x + -1x2)' equal to zero and attempt to solve: Simplifying -500 + 50x + -1x2 = 0 Solving -500 + 50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 500 + -50x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -50x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -50x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -50x + x2 = 0 + -500 -50x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -50x + x2 = -500 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -500 + 625 Reorder the terms: 625 + -50x + x2 = -500 + 625 Combine like terms: -500 + 625 = 125 625 + -50x + x2 = 125 Factor a perfect square on the left side: (x + -25)(x + -25) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -25) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -25 = 11.180339887 Simplifying x + -25 = 11.180339887 Reorder the terms: -25 + x = 11.180339887 Solving -25 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 11.180339887 + 25 Combine like terms: -25 + 25 = 0 0 + x = 11.180339887 + 25 x = 11.180339887 + 25 Combine like terms: 11.180339887 + 25 = 36.180339887 x = 36.180339887 Simplifying x = 36.180339887Subproblem 2
x + -25 = -11.180339887 Simplifying x + -25 = -11.180339887 Reorder the terms: -25 + x = -11.180339887 Solving -25 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -11.180339887 + 25 Combine like terms: -25 + 25 = 0 0 + x = -11.180339887 + 25 x = -11.180339887 + 25 Combine like terms: -11.180339887 + 25 = 13.819660113 x = 13.819660113 Simplifying x = 13.819660113Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.180339887, 13.819660113}Solution
x = {36.180339887, 13.819660113}
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