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Simplifying 25x + x2 = 625 Solving 25x + x2 = 625 Solving for variable 'x'. Reorder the terms: -625 + 25x + x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -625 + 25x + x2 = 0 Begin completing the square. 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 = 15.450849719 x = 15.450849719 Simplifying x = 15.450849719Subproblem 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 = -40.450849719 x = -40.450849719 Simplifying x = -40.450849719Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.450849719, -40.450849719}
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