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Simplifying x2 + -175x + 2500 = 0 Reorder the terms: 2500 + -175x + x2 = 0 Solving 2500 + -175x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -175x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -175x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -175x + x2 = 0 + -2500 -175x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -175x + x2 = -2500 The x term is -175x. Take half its coefficient (-87.5). Square it (7656.25) and add it to both sides. Add '7656.25' to each side of the equation. -175x + 7656.25 + x2 = -2500 + 7656.25 Reorder the terms: 7656.25 + -175x + x2 = -2500 + 7656.25 Combine like terms: -2500 + 7656.25 = 5156.25 7656.25 + -175x + x2 = 5156.25 Factor a perfect square on the left side: (x + -87.5)(x + -87.5) = 5156.25 Calculate the square root of the right side: 71.807033082 Break this problem into two subproblems by setting (x + -87.5) equal to 71.807033082 and -71.807033082.Subproblem 1
x + -87.5 = 71.807033082 Simplifying x + -87.5 = 71.807033082 Reorder the terms: -87.5 + x = 71.807033082 Solving -87.5 + x = 71.807033082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.5' to each side of the equation. -87.5 + 87.5 + x = 71.807033082 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + x = 71.807033082 + 87.5 x = 71.807033082 + 87.5 Combine like terms: 71.807033082 + 87.5 = 159.307033082 x = 159.307033082 Simplifying x = 159.307033082Subproblem 2
x + -87.5 = -71.807033082 Simplifying x + -87.5 = -71.807033082 Reorder the terms: -87.5 + x = -71.807033082 Solving -87.5 + x = -71.807033082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.5' to each side of the equation. -87.5 + 87.5 + x = -71.807033082 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + x = -71.807033082 + 87.5 x = -71.807033082 + 87.5 Combine like terms: -71.807033082 + 87.5 = 15.692966918 x = 15.692966918 Simplifying x = 15.692966918Solution
The solution to the problem is based on the solutions from the subproblems. x = {159.307033082, 15.692966918}
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