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Simplifying 2[(x + 4) * x] + 2[(x + 8) * x] + 2[(x + 4)(x + 8)] = 262 Reorder the terms: 2[(4 + x) * x] + 2[(x + 8) * x] + 2[(x + 4)(x + 8)] = 262 Reorder the terms for easier multiplication: 2[x(4 + x)] + 2[(x + 8) * x] + 2[(x + 4)(x + 8)] = 262 2[(4 * x + x * x)] + 2[(x + 8) * x] + 2[(x + 4)(x + 8)] = 262 2[(4x + x2)] + 2[(x + 8) * x] + 2[(x + 4)(x + 8)] = 262 [4x * 2 + x2 * 2] + 2[(x + 8) * x] + 2[(x + 4)(x + 8)] = 262 [8x + 2x2] + 2[(x + 8) * x] + 2[(x + 4)(x + 8)] = 262 Reorder the terms: 8x + 2x2 + 2[(8 + x) * x] + 2[(x + 4)(x + 8)] = 262 Reorder the terms for easier multiplication: 8x + 2x2 + 2[x(8 + x)] + 2[(x + 4)(x + 8)] = 262 8x + 2x2 + 2[(8 * x + x * x)] + 2[(x + 4)(x + 8)] = 262 8x + 2x2 + 2[(8x + x2)] + 2[(x + 4)(x + 8)] = 262 8x + 2x2 + [8x * 2 + x2 * 2] + 2[(x + 4)(x + 8)] = 262 8x + 2x2 + [16x + 2x2] + 2[(x + 4)(x + 8)] = 262 Reorder the terms: 8x + 2x2 + 16x + 2x2 + 2[(4 + x)(x + 8)] = 262 Reorder the terms: 8x + 2x2 + 16x + 2x2 + 2[(4 + x)(8 + x)] = 262 Multiply (4 + x) * (8 + x) 8x + 2x2 + 16x + 2x2 + 2[(4(8 + x) + x(8 + x))] = 262 8x + 2x2 + 16x + 2x2 + 2[((8 * 4 + x * 4) + x(8 + x))] = 262 8x + 2x2 + 16x + 2x2 + 2[((32 + 4x) + x(8 + x))] = 262 8x + 2x2 + 16x + 2x2 + 2[(32 + 4x + (8 * x + x * x))] = 262 8x + 2x2 + 16x + 2x2 + 2[(32 + 4x + (8x + x2))] = 262 Combine like terms: 4x + 8x = 12x 8x + 2x2 + 16x + 2x2 + 2[(32 + 12x + x2)] = 262 8x + 2x2 + 16x + 2x2 + [32 * 2 + 12x * 2 + x2 * 2] = 262 8x + 2x2 + 16x + 2x2 + [64 + 24x + 2x2] = 262 Reorder the terms: 64 + 8x + 16x + 24x + 2x2 + 2x2 + 2x2 = 262 Combine like terms: 8x + 16x = 24x 64 + 24x + 24x + 2x2 + 2x2 + 2x2 = 262 Combine like terms: 24x + 24x = 48x 64 + 48x + 2x2 + 2x2 + 2x2 = 262 Combine like terms: 2x2 + 2x2 = 4x2 64 + 48x + 4x2 + 2x2 = 262 Combine like terms: 4x2 + 2x2 = 6x2 64 + 48x + 6x2 = 262 Solving 64 + 48x + 6x2 = 262 Solving for variable 'x'. Reorder the terms: 64 + -262 + 48x + 6x2 = 262 + -262 Combine like terms: 64 + -262 = -198 -198 + 48x + 6x2 = 262 + -262 Combine like terms: 262 + -262 = 0 -198 + 48x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-33 + 8x + x2) = 0 Factor a trinomial. 6((-11 + -1x)(3 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-11, 3}
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