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Simplifying x(x + 2) = 124 Reorder the terms: x(2 + x) = 124 (2 * x + x * x) = 124 (2x + x2) = 124 Solving 2x + x2 = 124 Solving for variable 'x'. Reorder the terms: -124 + 2x + x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + 2x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 2x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 2x + x2 = 0 + 124 2x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 2x + x2 = 124 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 = 124 + 1 Reorder the terms: 1 + 2x + x2 = 124 + 1 Combine like terms: 124 + 1 = 125 1 + 2x + x2 = 125 Factor a perfect square on the left side: (x + 1)(x + 1) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 1) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 1 = 11.180339887 Simplifying x + 1 = 11.180339887 Reorder the terms: 1 + x = 11.180339887 Solving 1 + x = 11.180339887 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 = 11.180339887 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.180339887 + -1 x = 11.180339887 + -1 Combine like terms: 11.180339887 + -1 = 10.180339887 x = 10.180339887 Simplifying x = 10.180339887Subproblem 2
x + 1 = -11.180339887 Simplifying x + 1 = -11.180339887 Reorder the terms: 1 + x = -11.180339887 Solving 1 + x = -11.180339887 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 = -11.180339887 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.180339887 + -1 x = -11.180339887 + -1 Combine like terms: -11.180339887 + -1 = -12.180339887 x = -12.180339887 Simplifying x = -12.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.180339887, -12.180339887}
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