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Simplifying x2 + 32x + -12 = 0 Reorder the terms: -12 + 32x + x2 = 0 Solving -12 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 32x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 32x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 32x + x2 = 0 + 12 32x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 32x + x2 = 12 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 = 12 + 256 Reorder the terms: 256 + 32x + x2 = 12 + 256 Combine like terms: 12 + 256 = 268 256 + 32x + x2 = 268 Factor a perfect square on the left side: (x + 16)(x + 16) = 268 Calculate the square root of the right side: 16.370705544 Break this problem into two subproblems by setting (x + 16) equal to 16.370705544 and -16.370705544.Subproblem 1
x + 16 = 16.370705544 Simplifying x + 16 = 16.370705544 Reorder the terms: 16 + x = 16.370705544 Solving 16 + x = 16.370705544 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 = 16.370705544 + -16 Combine like terms: 16 + -16 = 0 0 + x = 16.370705544 + -16 x = 16.370705544 + -16 Combine like terms: 16.370705544 + -16 = 0.370705544 x = 0.370705544 Simplifying x = 0.370705544Subproblem 2
x + 16 = -16.370705544 Simplifying x + 16 = -16.370705544 Reorder the terms: 16 + x = -16.370705544 Solving 16 + x = -16.370705544 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 = -16.370705544 + -16 Combine like terms: 16 + -16 = 0 0 + x = -16.370705544 + -16 x = -16.370705544 + -16 Combine like terms: -16.370705544 + -16 = -32.370705544 x = -32.370705544 Simplifying x = -32.370705544Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.370705544, -32.370705544}
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