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Simplifying 237.25 + -25x + x2 = 156.25 Solving 237.25 + -25x + x2 = 156.25 Solving for variable 'x'. Reorder the terms: 237.25 + -156.25 + -25x + x2 = 156.25 + -156.25 Combine like terms: 237.25 + -156.25 = 81 81 + -25x + x2 = 156.25 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 81 + -25x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -25x + -81 + x2 = 0.00 + -81 Reorder the terms: 81 + -81 + -25x + x2 = 0.00 + -81 Combine like terms: 81 + -81 = 0 0 + -25x + x2 = 0.00 + -81 -25x + x2 = 0.00 + -81 Combine like terms: 0.00 + -81 = -81 -25x + x2 = -81 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 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -81 + 156.25 Combine like terms: -81 + 156.25 = 75.25 156.25 + -25x + x2 = 75.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (x + -12.5) equal to 8.674675786 and -8.674675786.Subproblem 1
x + -12.5 = 8.674675786 Simplifying x + -12.5 = 8.674675786 Reorder the terms: -12.5 + x = 8.674675786 Solving -12.5 + x = 8.674675786 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 = 8.674675786 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 8.674675786 + 12.5 x = 8.674675786 + 12.5 Combine like terms: 8.674675786 + 12.5 = 21.174675786 x = 21.174675786 Simplifying x = 21.174675786Subproblem 2
x + -12.5 = -8.674675786 Simplifying x + -12.5 = -8.674675786 Reorder the terms: -12.5 + x = -8.674675786 Solving -12.5 + x = -8.674675786 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 = -8.674675786 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -8.674675786 + 12.5 x = -8.674675786 + 12.5 Combine like terms: -8.674675786 + 12.5 = 3.825324214 x = 3.825324214 Simplifying x = 3.825324214Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.174675786, 3.825324214}
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