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