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Simplifying (5x + -4)(5x + -4) + (x + 8)(x + 8) = (5x)(5x) Reorder the terms: (-4 + 5x)(5x + -4) + (x + 8)(x + 8) = (5x)(5x) Reorder the terms: (-4 + 5x)(-4 + 5x) + (x + 8)(x + 8) = (5x)(5x) Multiply (-4 + 5x) * (-4 + 5x) (-4(-4 + 5x) + 5x * (-4 + 5x)) + (x + 8)(x + 8) = (5x)(5x) ((-4 * -4 + 5x * -4) + 5x * (-4 + 5x)) + (x + 8)(x + 8) = (5x)(5x) ((16 + -20x) + 5x * (-4 + 5x)) + (x + 8)(x + 8) = (5x)(5x) (16 + -20x + (-4 * 5x + 5x * 5x)) + (x + 8)(x + 8) = (5x)(5x) (16 + -20x + (-20x + 25x2)) + (x + 8)(x + 8) = (5x)(5x) Combine like terms: -20x + -20x = -40x (16 + -40x + 25x2) + (x + 8)(x + 8) = (5x)(5x) Reorder the terms: 16 + -40x + 25x2 + (8 + x)(x + 8) = (5x)(5x) Reorder the terms: 16 + -40x + 25x2 + (8 + x)(8 + x) = (5x)(5x) Multiply (8 + x) * (8 + x) 16 + -40x + 25x2 + (8(8 + x) + x(8 + x)) = (5x)(5x) 16 + -40x + 25x2 + ((8 * 8 + x * 8) + x(8 + x)) = (5x)(5x) 16 + -40x + 25x2 + ((64 + 8x) + x(8 + x)) = (5x)(5x) 16 + -40x + 25x2 + (64 + 8x + (8 * x + x * x)) = (5x)(5x) 16 + -40x + 25x2 + (64 + 8x + (8x + x2)) = (5x)(5x) Combine like terms: 8x + 8x = 16x 16 + -40x + 25x2 + (64 + 16x + x2) = (5x)(5x) Reorder the terms: 16 + 64 + -40x + 16x + 25x2 + x2 = (5x)(5x) Combine like terms: 16 + 64 = 80 80 + -40x + 16x + 25x2 + x2 = (5x)(5x) Combine like terms: -40x + 16x = -24x 80 + -24x + 25x2 + x2 = (5x)(5x) Combine like terms: 25x2 + x2 = 26x2 80 + -24x + 26x2 = (5x)(5x) Remove parenthesis around (5x) 80 + -24x + 26x2 = 5x(5x) Remove parenthesis around (5x) 80 + -24x + 26x2 = 5x * 5x Reorder the terms for easier multiplication: 80 + -24x + 26x2 = 5 * 5x * x Multiply 5 * 5 80 + -24x + 26x2 = 25x * x Multiply x * x 80 + -24x + 26x2 = 25x2 Solving 80 + -24x + 26x2 = 25x2 Solving for variable 'x'. Combine like terms: 26x2 + -25x2 = 1x2 80 + -24x + 1x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 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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