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Simplifying x2 + 32x + 126 = 0 Reorder the terms: 126 + 32x + x2 = 0 Solving 126 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-126' to each side of the equation. 126 + 32x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + 32x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + 32x + x2 = 0 + -126 32x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 32x + x2 = -126 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -126 + 256 Reorder the terms: 256 + 32x + x2 = -126 + 256 Combine like terms: -126 + 256 = 130 256 + 32x + x2 = 130 Factor a perfect square on the left side: (x + 16)(x + 16) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 16) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 16 = 11.401754251 Simplifying x + 16 = 11.401754251 Reorder the terms: 16 + x = 11.401754251 Solving 16 + x = 11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 11.401754251 + -16 Combine like terms: 16 + -16 = 0 0 + x = 11.401754251 + -16 x = 11.401754251 + -16 Combine like terms: 11.401754251 + -16 = -4.598245749 x = -4.598245749 Simplifying x = -4.598245749Subproblem 2
x + 16 = -11.401754251 Simplifying x + 16 = -11.401754251 Reorder the terms: 16 + x = -11.401754251 Solving 16 + x = -11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -11.401754251 + -16 Combine like terms: 16 + -16 = 0 0 + x = -11.401754251 + -16 x = -11.401754251 + -16 Combine like terms: -11.401754251 + -16 = -27.401754251 x = -27.401754251 Simplifying x = -27.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.598245749, -27.401754251}
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