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Simplifying (8x + 2)(8x + 16) = 0 Reorder the terms: (2 + 8x)(8x + 16) = 0 Reorder the terms: (2 + 8x)(16 + 8x) = 0 Multiply (2 + 8x) * (16 + 8x) (2(16 + 8x) + 8x * (16 + 8x)) = 0 ((16 * 2 + 8x * 2) + 8x * (16 + 8x)) = 0 ((32 + 16x) + 8x * (16 + 8x)) = 0 (32 + 16x + (16 * 8x + 8x * 8x)) = 0 (32 + 16x + (128x + 64x2)) = 0 Combine like terms: 16x + 128x = 144x (32 + 144x + 64x2) = 0 Solving 32 + 144x + 64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(2 + 9x + 4x2) = 0 Factor a trinomial. 16((2 + x)(1 + 4x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {-2, -0.25}
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