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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 = 382 256 + 32x + x2 = 382 Factor a perfect square on the left side: (x + 16)(x + 16) = 382 Calculate the square root of the right side: 19.544820286 Break this problem into two subproblems by setting (x + 16) equal to 19.544820286 and -19.544820286.Subproblem 1
x + 16 = 19.544820286 Simplifying x + 16 = 19.544820286 Reorder the terms: 16 + x = 19.544820286 Solving 16 + x = 19.544820286 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 = 19.544820286 + -16 Combine like terms: 16 + -16 = 0 0 + x = 19.544820286 + -16 x = 19.544820286 + -16 Combine like terms: 19.544820286 + -16 = 3.544820286 x = 3.544820286 Simplifying x = 3.544820286Subproblem 2
x + 16 = -19.544820286 Simplifying x + 16 = -19.544820286 Reorder the terms: 16 + x = -19.544820286 Solving 16 + x = -19.544820286 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 = -19.544820286 + -16 Combine like terms: 16 + -16 = 0 0 + x = -19.544820286 + -16 x = -19.544820286 + -16 Combine like terms: -19.544820286 + -16 = -35.544820286 x = -35.544820286 Simplifying x = -35.544820286Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.544820286, -35.544820286}
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