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Simplifying x2 + -2x + -125 = 0 Reorder the terms: -125 + -2x + x2 = 0 Solving -125 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -2x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -2x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -2x + x2 = 0 + 125 -2x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -2x + x2 = 125 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 125 + 1 Reorder the terms: 1 + -2x + x2 = 125 + 1 Combine like terms: 125 + 1 = 126 1 + -2x + x2 = 126 Factor a perfect square on the left side: (x + -1)(x + -1) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + -1) equal to 11.22497216 and -11.22497216.Subproblem 1
x + -1 = 11.22497216 Simplifying x + -1 = 11.22497216 Reorder the terms: -1 + x = 11.22497216 Solving -1 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 11.22497216 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.22497216 + 1 x = 11.22497216 + 1 Combine like terms: 11.22497216 + 1 = 12.22497216 x = 12.22497216 Simplifying x = 12.22497216Subproblem 2
x + -1 = -11.22497216 Simplifying x + -1 = -11.22497216 Reorder the terms: -1 + x = -11.22497216 Solving -1 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -11.22497216 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.22497216 + 1 x = -11.22497216 + 1 Combine like terms: -11.22497216 + 1 = -10.22497216 x = -10.22497216 Simplifying x = -10.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.22497216, -10.22497216}
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