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Simplifying x2 + -25x = 5000 Reorder the terms: -25x + x2 = 5000 Solving -25x + x2 = 5000 Solving for variable 'x'. Reorder the terms: -5000 + -25x + x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5000 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + -25x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + -25x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + -25x + x2 = 0 + 5000 -25x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 -25x + x2 = 5000 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 5000 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 5000 + 156.25 Combine like terms: 5000 + 156.25 = 5156.25 156.25 + -25x + x2 = 5156.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 5156.25 Calculate the square root of the right side: 71.807033082 Break this problem into two subproblems by setting (x + -12.5) equal to 71.807033082 and -71.807033082.Subproblem 1
x + -12.5 = 71.807033082 Simplifying x + -12.5 = 71.807033082 Reorder the terms: -12.5 + x = 71.807033082 Solving -12.5 + x = 71.807033082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 71.807033082 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 71.807033082 + 12.5 x = 71.807033082 + 12.5 Combine like terms: 71.807033082 + 12.5 = 84.307033082 x = 84.307033082 Simplifying x = 84.307033082Subproblem 2
x + -12.5 = -71.807033082 Simplifying x + -12.5 = -71.807033082 Reorder the terms: -12.5 + x = -71.807033082 Solving -12.5 + x = -71.807033082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -71.807033082 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -71.807033082 + 12.5 x = -71.807033082 + 12.5 Combine like terms: -71.807033082 + 12.5 = -59.307033082 x = -59.307033082 Simplifying x = -59.307033082Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.307033082, -59.307033082}
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