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Simplifying (5x + 16)(5x + 16) = (8x + -14)(8x + -14) Reorder the terms: (16 + 5x)(5x + 16) = (8x + -14)(8x + -14) Reorder the terms: (16 + 5x)(16 + 5x) = (8x + -14)(8x + -14) Multiply (16 + 5x) * (16 + 5x) (16(16 + 5x) + 5x * (16 + 5x)) = (8x + -14)(8x + -14) ((16 * 16 + 5x * 16) + 5x * (16 + 5x)) = (8x + -14)(8x + -14) ((256 + 80x) + 5x * (16 + 5x)) = (8x + -14)(8x + -14) (256 + 80x + (16 * 5x + 5x * 5x)) = (8x + -14)(8x + -14) (256 + 80x + (80x + 25x2)) = (8x + -14)(8x + -14) Combine like terms: 80x + 80x = 160x (256 + 160x + 25x2) = (8x + -14)(8x + -14) Reorder the terms: 256 + 160x + 25x2 = (-14 + 8x)(8x + -14) Reorder the terms: 256 + 160x + 25x2 = (-14 + 8x)(-14 + 8x) Multiply (-14 + 8x) * (-14 + 8x) 256 + 160x + 25x2 = (-14(-14 + 8x) + 8x * (-14 + 8x)) 256 + 160x + 25x2 = ((-14 * -14 + 8x * -14) + 8x * (-14 + 8x)) 256 + 160x + 25x2 = ((196 + -112x) + 8x * (-14 + 8x)) 256 + 160x + 25x2 = (196 + -112x + (-14 * 8x + 8x * 8x)) 256 + 160x + 25x2 = (196 + -112x + (-112x + 64x2)) Combine like terms: -112x + -112x = -224x 256 + 160x + 25x2 = (196 + -224x + 64x2) Solving 256 + 160x + 25x2 = 196 + -224x + 64x2 Solving for variable 'x'. Reorder the terms: 256 + -196 + 160x + 224x + 25x2 + -64x2 = 196 + -224x + 64x2 + -196 + 224x + -64x2 Combine like terms: 256 + -196 = 60 60 + 160x + 224x + 25x2 + -64x2 = 196 + -224x + 64x2 + -196 + 224x + -64x2 Combine like terms: 160x + 224x = 384x 60 + 384x + 25x2 + -64x2 = 196 + -224x + 64x2 + -196 + 224x + -64x2 Combine like terms: 25x2 + -64x2 = -39x2 60 + 384x + -39x2 = 196 + -224x + 64x2 + -196 + 224x + -64x2 Reorder the terms: 60 + 384x + -39x2 = 196 + -196 + -224x + 224x + 64x2 + -64x2 Combine like terms: 196 + -196 = 0 60 + 384x + -39x2 = 0 + -224x + 224x + 64x2 + -64x2 60 + 384x + -39x2 = -224x + 224x + 64x2 + -64x2 Combine like terms: -224x + 224x = 0 60 + 384x + -39x2 = 0 + 64x2 + -64x2 60 + 384x + -39x2 = 64x2 + -64x2 Combine like terms: 64x2 + -64x2 = 0 60 + 384x + -39x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(20 + 128x + -13x2) = 0 Factor a trinomial. 3((10 + -1x)(2 + 13x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(2 + 13x)' equal to zero and attempt to solve: Simplifying 2 + 13x = 0 Solving 2 + 13x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 13x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 13x = 0 + -2 13x = 0 + -2 Combine like terms: 0 + -2 = -2 13x = -2 Divide each side by '13'. x = -0.1538461538 Simplifying x = -0.1538461538Solution
x = {10, -0.1538461538}
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