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Simplifying (4x + 2)(4x + 2) = 36 Reorder the terms: (2 + 4x)(4x + 2) = 36 Reorder the terms: (2 + 4x)(2 + 4x) = 36 Multiply (2 + 4x) * (2 + 4x) (2(2 + 4x) + 4x * (2 + 4x)) = 36 ((2 * 2 + 4x * 2) + 4x * (2 + 4x)) = 36 ((4 + 8x) + 4x * (2 + 4x)) = 36 (4 + 8x + (2 * 4x + 4x * 4x)) = 36 (4 + 8x + (8x + 16x2)) = 36 Combine like terms: 8x + 8x = 16x (4 + 16x + 16x2) = 36 Solving 4 + 16x + 16x2 = 36 Solving for variable 'x'. Reorder the terms: 4 + -36 + 16x + 16x2 = 36 + -36 Combine like terms: 4 + -36 = -32 -32 + 16x + 16x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -32 + 16x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-2 + x + x2) = 0 Factor a trinomial. 16((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2, 1}
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