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Simplifying (x) = x2 + 4x + -32x + -8 x = x2 + 4x + -32x + -8 Reorder the terms: x = -8 + 4x + -32x + x2 Combine like terms: 4x + -32x = -28x x = -8 + -28x + x2 Solving x = -8 + -28x + x2 Solving for variable 'x'. Reorder the terms: 8 + x + 28x + -1x2 = -8 + -28x + x2 + 8 + 28x + -1x2 Combine like terms: x + 28x = 29x 8 + 29x + -1x2 = -8 + -28x + x2 + 8 + 28x + -1x2 Reorder the terms: 8 + 29x + -1x2 = -8 + 8 + -28x + 28x + x2 + -1x2 Combine like terms: -8 + 8 = 0 8 + 29x + -1x2 = 0 + -28x + 28x + x2 + -1x2 8 + 29x + -1x2 = -28x + 28x + x2 + -1x2 Combine like terms: -28x + 28x = 0 8 + 29x + -1x2 = 0 + x2 + -1x2 8 + 29x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + 29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -29x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -29x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -29x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -29x + x2 = 0 + 8 -29x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -29x + x2 = 8 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = 8 + 210.25 Reorder the terms: 210.25 + -29x + x2 = 8 + 210.25 Combine like terms: 8 + 210.25 = 218.25 210.25 + -29x + x2 = 218.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 218.25 Calculate the square root of the right side: 14.773286703 Break this problem into two subproblems by setting (x + -14.5) equal to 14.773286703 and -14.773286703.Subproblem 1
x + -14.5 = 14.773286703 Simplifying x + -14.5 = 14.773286703 Reorder the terms: -14.5 + x = 14.773286703 Solving -14.5 + x = 14.773286703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 14.773286703 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 14.773286703 + 14.5 x = 14.773286703 + 14.5 Combine like terms: 14.773286703 + 14.5 = 29.273286703 x = 29.273286703 Simplifying x = 29.273286703Subproblem 2
x + -14.5 = -14.773286703 Simplifying x + -14.5 = -14.773286703 Reorder the terms: -14.5 + x = -14.773286703 Solving -14.5 + x = -14.773286703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -14.773286703 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -14.773286703 + 14.5 x = -14.773286703 + 14.5 Combine like terms: -14.773286703 + 14.5 = -0.273286703 x = -0.273286703 Simplifying x = -0.273286703Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.273286703, -0.273286703}
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