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Simplifying -1x2 + 25x + 625 = 0 Reorder the terms: 625 + 25x + -1x2 = 0 Solving 625 + 25x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -625 + -25x + x2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + -25x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + -25x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -25x + x2 = 0 + 625 -25x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 -25x + x2 = 625 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 = 625 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 625 + 156.25 Combine like terms: 625 + 156.25 = 781.25 156.25 + -25x + x2 = 781.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 781.25 Calculate the square root of the right side: 27.950849719 Break this problem into two subproblems by setting (x + -12.5) equal to 27.950849719 and -27.950849719.Subproblem 1
x + -12.5 = 27.950849719 Simplifying x + -12.5 = 27.950849719 Reorder the terms: -12.5 + x = 27.950849719 Solving -12.5 + x = 27.950849719 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 = 27.950849719 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 27.950849719 + 12.5 x = 27.950849719 + 12.5 Combine like terms: 27.950849719 + 12.5 = 40.450849719 x = 40.450849719 Simplifying x = 40.450849719Subproblem 2
x + -12.5 = -27.950849719 Simplifying x + -12.5 = -27.950849719 Reorder the terms: -12.5 + x = -27.950849719 Solving -12.5 + x = -27.950849719 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 = -27.950849719 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -27.950849719 + 12.5 x = -27.950849719 + 12.5 Combine like terms: -27.950849719 + 12.5 = -15.450849719 x = -15.450849719 Simplifying x = -15.450849719Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.450849719, -15.450849719}
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