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Simplifying x2 + (2x + 8)(2x + 8) = (3x + -8)(3x + -8) Reorder the terms: x2 + (8 + 2x)(2x + 8) = (3x + -8)(3x + -8) Reorder the terms: x2 + (8 + 2x)(8 + 2x) = (3x + -8)(3x + -8) Multiply (8 + 2x) * (8 + 2x) x2 + (8(8 + 2x) + 2x * (8 + 2x)) = (3x + -8)(3x + -8) x2 + ((8 * 8 + 2x * 8) + 2x * (8 + 2x)) = (3x + -8)(3x + -8) x2 + ((64 + 16x) + 2x * (8 + 2x)) = (3x + -8)(3x + -8) x2 + (64 + 16x + (8 * 2x + 2x * 2x)) = (3x + -8)(3x + -8) x2 + (64 + 16x + (16x + 4x2)) = (3x + -8)(3x + -8) Combine like terms: 16x + 16x = 32x x2 + (64 + 32x + 4x2) = (3x + -8)(3x + -8) Reorder the terms: 64 + 32x + x2 + 4x2 = (3x + -8)(3x + -8) Combine like terms: x2 + 4x2 = 5x2 64 + 32x + 5x2 = (3x + -8)(3x + -8) Reorder the terms: 64 + 32x + 5x2 = (-8 + 3x)(3x + -8) Reorder the terms: 64 + 32x + 5x2 = (-8 + 3x)(-8 + 3x) Multiply (-8 + 3x) * (-8 + 3x) 64 + 32x + 5x2 = (-8(-8 + 3x) + 3x * (-8 + 3x)) 64 + 32x + 5x2 = ((-8 * -8 + 3x * -8) + 3x * (-8 + 3x)) 64 + 32x + 5x2 = ((64 + -24x) + 3x * (-8 + 3x)) 64 + 32x + 5x2 = (64 + -24x + (-8 * 3x + 3x * 3x)) 64 + 32x + 5x2 = (64 + -24x + (-24x + 9x2)) Combine like terms: -24x + -24x = -48x 64 + 32x + 5x2 = (64 + -48x + 9x2) Add '-64' to each side of the equation. 64 + 32x + -64 + 5x2 = 64 + -48x + -64 + 9x2 Reorder the terms: 64 + -64 + 32x + 5x2 = 64 + -48x + -64 + 9x2 Combine like terms: 64 + -64 = 0 0 + 32x + 5x2 = 64 + -48x + -64 + 9x2 32x + 5x2 = 64 + -48x + -64 + 9x2 Reorder the terms: 32x + 5x2 = 64 + -64 + -48x + 9x2 Combine like terms: 64 + -64 = 0 32x + 5x2 = 0 + -48x + 9x2 32x + 5x2 = -48x + 9x2 Solving 32x + 5x2 = -48x + 9x2 Solving for variable 'x'. Reorder the terms: 32x + 48x + 5x2 + -9x2 = -48x + 9x2 + 48x + -9x2 Combine like terms: 32x + 48x = 80x 80x + 5x2 + -9x2 = -48x + 9x2 + 48x + -9x2 Combine like terms: 5x2 + -9x2 = -4x2 80x + -4x2 = -48x + 9x2 + 48x + -9x2 Reorder the terms: 80x + -4x2 = -48x + 48x + 9x2 + -9x2 Combine like terms: -48x + 48x = 0 80x + -4x2 = 0 + 9x2 + -9x2 80x + -4x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(20 + -1x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {0, 20}
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