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Simplifying 237.5 + -25x + x2 = 156.25 Solving 237.5 + -25x + x2 = 156.25 Solving for variable 'x'. Reorder the terms: 237.5 + -156.25 + -25x + x2 = 156.25 + -156.25 Combine like terms: 237.5 + -156.25 = 81.25 81.25 + -25x + x2 = 156.25 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 81.25 + -25x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-81.25' to each side of the equation. 81.25 + -25x + -81.25 + x2 = 0.00 + -81.25 Reorder the terms: 81.25 + -81.25 + -25x + x2 = 0.00 + -81.25 Combine like terms: 81.25 + -81.25 = 0.00 0.00 + -25x + x2 = 0.00 + -81.25 -25x + x2 = 0.00 + -81.25 Combine like terms: 0.00 + -81.25 = -81.25 -25x + x2 = -81.25 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 = -81.25 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -81.25 + 156.25 Combine like terms: -81.25 + 156.25 = 75 156.25 + -25x + x2 = 75 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -12.5) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -12.5 = 8.660254038 Simplifying x + -12.5 = 8.660254038 Reorder the terms: -12.5 + x = 8.660254038 Solving -12.5 + x = 8.660254038 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 = 8.660254038 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 8.660254038 + 12.5 x = 8.660254038 + 12.5 Combine like terms: 8.660254038 + 12.5 = 21.160254038 x = 21.160254038 Simplifying x = 21.160254038Subproblem 2
x + -12.5 = -8.660254038 Simplifying x + -12.5 = -8.660254038 Reorder the terms: -12.5 + x = -8.660254038 Solving -12.5 + x = -8.660254038 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 = -8.660254038 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -8.660254038 + 12.5 x = -8.660254038 + 12.5 Combine like terms: -8.660254038 + 12.5 = 3.839745962 x = 3.839745962 Simplifying x = 3.839745962Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.160254038, 3.839745962}
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