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Simplifying (4x + 2)(4x + 2) = 0 Reorder the terms: (2 + 4x)(4x + 2) = 0 Reorder the terms: (2 + 4x)(2 + 4x) = 0 Multiply (2 + 4x) * (2 + 4x) (2(2 + 4x) + 4x * (2 + 4x)) = 0 ((2 * 2 + 4x * 2) + 4x * (2 + 4x)) = 0 ((4 + 8x) + 4x * (2 + 4x)) = 0 (4 + 8x + (2 * 4x + 4x * 4x)) = 0 (4 + 8x + (8x + 16x2)) = 0 Combine like terms: 8x + 8x = 16x (4 + 16x + 16x2) = 0 Solving 4 + 16x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 4x + 4x2) = 0 Factor a trinomial. 4((1 + 2x)(1 + 2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-0.5, -0.5}
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