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Simplifying x2 + 32x + 128 = 0 Reorder the terms: 128 + 32x + x2 = 0 Solving 128 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-128' to each side of the equation. 128 + 32x + -128 + x2 = 0 + -128 Reorder the terms: 128 + -128 + 32x + x2 = 0 + -128 Combine like terms: 128 + -128 = 0 0 + 32x + x2 = 0 + -128 32x + x2 = 0 + -128 Combine like terms: 0 + -128 = -128 32x + x2 = -128 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 = -128 + 256 Reorder the terms: 256 + 32x + x2 = -128 + 256 Combine like terms: -128 + 256 = 128 256 + 32x + x2 = 128 Factor a perfect square on the left side: (x + 16)(x + 16) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + 16) equal to 11.313708499 and -11.313708499.Subproblem 1
x + 16 = 11.313708499 Simplifying x + 16 = 11.313708499 Reorder the terms: 16 + x = 11.313708499 Solving 16 + x = 11.313708499 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 = 11.313708499 + -16 Combine like terms: 16 + -16 = 0 0 + x = 11.313708499 + -16 x = 11.313708499 + -16 Combine like terms: 11.313708499 + -16 = -4.686291501 x = -4.686291501 Simplifying x = -4.686291501Subproblem 2
x + 16 = -11.313708499 Simplifying x + 16 = -11.313708499 Reorder the terms: 16 + x = -11.313708499 Solving 16 + x = -11.313708499 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 = -11.313708499 + -16 Combine like terms: 16 + -16 = 0 0 + x = -11.313708499 + -16 x = -11.313708499 + -16 Combine like terms: -11.313708499 + -16 = -27.313708499 x = -27.313708499 Simplifying x = -27.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.686291501, -27.313708499}
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