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Simplifying -2x2 + -64x + -112 = 0 Reorder the terms: -112 + -64x + -2x2 = 0 Solving -112 + -64x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(56 + 32x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(56 + 32x + x2)' equal to zero and attempt to solve: Simplifying 56 + 32x + x2 = 0 Solving 56 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 32x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + 32x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 32x + x2 = 0 + -56 32x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 32x + x2 = -56 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 = -56 + 256 Reorder the terms: 256 + 32x + x2 = -56 + 256 Combine like terms: -56 + 256 = 200 256 + 32x + x2 = 200 Factor a perfect square on the left side: (x + 16)(x + 16) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 16) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 16 = 14.142135624 Simplifying x + 16 = 14.142135624 Reorder the terms: 16 + x = 14.142135624 Solving 16 + x = 14.142135624 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 = 14.142135624 + -16 Combine like terms: 16 + -16 = 0 0 + x = 14.142135624 + -16 x = 14.142135624 + -16 Combine like terms: 14.142135624 + -16 = -1.857864376 x = -1.857864376 Simplifying x = -1.857864376Subproblem 2
x + 16 = -14.142135624 Simplifying x + 16 = -14.142135624 Reorder the terms: 16 + x = -14.142135624 Solving 16 + x = -14.142135624 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 = -14.142135624 + -16 Combine like terms: 16 + -16 = 0 0 + x = -14.142135624 + -16 x = -14.142135624 + -16 Combine like terms: -14.142135624 + -16 = -30.142135624 x = -30.142135624 Simplifying x = -30.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.857864376, -30.142135624}Solution
x = {-1.857864376, -30.142135624}
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