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Simplifying (2x + 4)(2x + 4) = 36 Reorder the terms: (4 + 2x)(2x + 4) = 36 Reorder the terms: (4 + 2x)(4 + 2x) = 36 Multiply (4 + 2x) * (4 + 2x) (4(4 + 2x) + 2x * (4 + 2x)) = 36 ((4 * 4 + 2x * 4) + 2x * (4 + 2x)) = 36 ((16 + 8x) + 2x * (4 + 2x)) = 36 (16 + 8x + (4 * 2x + 2x * 2x)) = 36 (16 + 8x + (8x + 4x2)) = 36 Combine like terms: 8x + 8x = 16x (16 + 16x + 4x2) = 36 Solving 16 + 16x + 4x2 = 36 Solving for variable 'x'. Reorder the terms: 16 + -36 + 16x + 4x2 = 36 + -36 Combine like terms: 16 + -36 = -20 -20 + 16x + 4x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -20 + 16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 4x + x2) = 0 Factor a trinomial. 4((-5 + -1x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 1}
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