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Simplifying x2 + 20x + 250 = x(75 + -1x) Reorder the terms: 250 + 20x + x2 = x(75 + -1x) 250 + 20x + x2 = (75 * x + -1x * x) 250 + 20x + x2 = (75x + -1x2) Solving 250 + 20x + x2 = 75x + -1x2 Solving for variable 'x'. Reorder the terms: 250 + 20x + -75x + x2 + x2 = 75x + -1x2 + -75x + x2 Combine like terms: 20x + -75x = -55x 250 + -55x + x2 + x2 = 75x + -1x2 + -75x + x2 Combine like terms: x2 + x2 = 2x2 250 + -55x + 2x2 = 75x + -1x2 + -75x + x2 Reorder the terms: 250 + -55x + 2x2 = 75x + -75x + -1x2 + x2 Combine like terms: 75x + -75x = 0 250 + -55x + 2x2 = 0 + -1x2 + x2 250 + -55x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 250 + -55x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 125 + -27.5x + x2 = 0 Move the constant term to the right: Add '-125' to each side of the equation. 125 + -27.5x + -125 + x2 = 0 + -125 Reorder the terms: 125 + -125 + -27.5x + x2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -27.5x + x2 = 0 + -125 -27.5x + x2 = 0 + -125 Combine like terms: 0 + -125 = -125 -27.5x + x2 = -125 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = -125 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = -125 + 189.0625 Combine like terms: -125 + 189.0625 = 64.0625 189.0625 + -27.5x + x2 = 64.0625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 64.0625 Calculate the square root of the right side: 8.003905297 Break this problem into two subproblems by setting (x + -13.75) equal to 8.003905297 and -8.003905297.Subproblem 1
x + -13.75 = 8.003905297 Simplifying x + -13.75 = 8.003905297 Reorder the terms: -13.75 + x = 8.003905297 Solving -13.75 + x = 8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 8.003905297 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 8.003905297 + 13.75 x = 8.003905297 + 13.75 Combine like terms: 8.003905297 + 13.75 = 21.753905297 x = 21.753905297 Simplifying x = 21.753905297Subproblem 2
x + -13.75 = -8.003905297 Simplifying x + -13.75 = -8.003905297 Reorder the terms: -13.75 + x = -8.003905297 Solving -13.75 + x = -8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -8.003905297 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -8.003905297 + 13.75 x = -8.003905297 + 13.75 Combine like terms: -8.003905297 + 13.75 = 5.746094703 x = 5.746094703 Simplifying x = 5.746094703Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.753905297, 5.746094703}
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