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Simplifying 2x2 + 16x + -32 = 1008 Reorder the terms: -32 + 16x + 2x2 = 1008 Solving -32 + 16x + 2x2 = 1008 Solving for variable 'x'. Reorder the terms: -32 + -1008 + 16x + 2x2 = 1008 + -1008 Combine like terms: -32 + -1008 = -1040 -1040 + 16x + 2x2 = 1008 + -1008 Combine like terms: 1008 + -1008 = 0 -1040 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-520 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-520 + 8x + x2)' equal to zero and attempt to solve: Simplifying -520 + 8x + x2 = 0 Solving -520 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '520' to each side of the equation. -520 + 8x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + 8x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + 8x + x2 = 0 + 520 8x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 8x + x2 = 520 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 520 + 16 Reorder the terms: 16 + 8x + x2 = 520 + 16 Combine like terms: 520 + 16 = 536 16 + 8x + x2 = 536 Factor a perfect square on the left side: (x + 4)(x + 4) = 536 Calculate the square root of the right side: 23.151673806 Break this problem into two subproblems by setting (x + 4) equal to 23.151673806 and -23.151673806.Subproblem 1
x + 4 = 23.151673806 Simplifying x + 4 = 23.151673806 Reorder the terms: 4 + x = 23.151673806 Solving 4 + x = 23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 23.151673806 + -4 Combine like terms: 4 + -4 = 0 0 + x = 23.151673806 + -4 x = 23.151673806 + -4 Combine like terms: 23.151673806 + -4 = 19.151673806 x = 19.151673806 Simplifying x = 19.151673806Subproblem 2
x + 4 = -23.151673806 Simplifying x + 4 = -23.151673806 Reorder the terms: 4 + x = -23.151673806 Solving 4 + x = -23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -23.151673806 + -4 Combine like terms: 4 + -4 = 0 0 + x = -23.151673806 + -4 x = -23.151673806 + -4 Combine like terms: -23.151673806 + -4 = -27.151673806 x = -27.151673806 Simplifying x = -27.151673806Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.151673806, -27.151673806}Solution
x = {19.151673806, -27.151673806}
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