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Simplifying x2 + -32x + -140 = 0 Reorder the terms: -140 + -32x + x2 = 0 Solving -140 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -32x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -32x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -32x + x2 = 0 + 140 -32x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -32x + x2 = 140 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 = 140 + 256 Reorder the terms: 256 + -32x + x2 = 140 + 256 Combine like terms: 140 + 256 = 396 256 + -32x + x2 = 396 Factor a perfect square on the left side: (x + -16)(x + -16) = 396 Calculate the square root of the right side: 19.899748742 Break this problem into two subproblems by setting (x + -16) equal to 19.899748742 and -19.899748742.Subproblem 1
x + -16 = 19.899748742 Simplifying x + -16 = 19.899748742 Reorder the terms: -16 + x = 19.899748742 Solving -16 + x = 19.899748742 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 = 19.899748742 + 16 Combine like terms: -16 + 16 = 0 0 + x = 19.899748742 + 16 x = 19.899748742 + 16 Combine like terms: 19.899748742 + 16 = 35.899748742 x = 35.899748742 Simplifying x = 35.899748742Subproblem 2
x + -16 = -19.899748742 Simplifying x + -16 = -19.899748742 Reorder the terms: -16 + x = -19.899748742 Solving -16 + x = -19.899748742 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 = -19.899748742 + 16 Combine like terms: -16 + 16 = 0 0 + x = -19.899748742 + 16 x = -19.899748742 + 16 Combine like terms: -19.899748742 + 16 = -3.899748742 x = -3.899748742 Simplifying x = -3.899748742Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.899748742, -3.899748742}
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