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Simplifying x2 + -32x + 120 = 0 Reorder the terms: 120 + -32x + x2 = 0 Solving 120 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -32x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -32x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -32x + x2 = 0 + -120 -32x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -32x + x2 = -120 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 = -120 + 256 Reorder the terms: 256 + -32x + x2 = -120 + 256 Combine like terms: -120 + 256 = 136 256 + -32x + x2 = 136 Factor a perfect square on the left side: (x + -16)(x + -16) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + -16) equal to 11.66190379 and -11.66190379.Subproblem 1
x + -16 = 11.66190379 Simplifying x + -16 = 11.66190379 Reorder the terms: -16 + x = 11.66190379 Solving -16 + x = 11.66190379 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 = 11.66190379 + 16 Combine like terms: -16 + 16 = 0 0 + x = 11.66190379 + 16 x = 11.66190379 + 16 Combine like terms: 11.66190379 + 16 = 27.66190379 x = 27.66190379 Simplifying x = 27.66190379Subproblem 2
x + -16 = -11.66190379 Simplifying x + -16 = -11.66190379 Reorder the terms: -16 + x = -11.66190379 Solving -16 + x = -11.66190379 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 = -11.66190379 + 16 Combine like terms: -16 + 16 = 0 0 + x = -11.66190379 + 16 x = -11.66190379 + 16 Combine like terms: -11.66190379 + 16 = 4.33809621 x = 4.33809621 Simplifying x = 4.33809621Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.66190379, 4.33809621}
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