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Simplifying (2x + 1)(2x + 1) = 16 Reorder the terms: (1 + 2x)(2x + 1) = 16 Reorder the terms: (1 + 2x)(1 + 2x) = 16 Multiply (1 + 2x) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x)) = 16 ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 16 ((1 + 2x) + 2x * (1 + 2x)) = 16 (1 + 2x + (1 * 2x + 2x * 2x)) = 16 (1 + 2x + (2x + 4x2)) = 16 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2) = 16 Solving 1 + 4x + 4x2 = 16 Solving for variable 'x'. Reorder the terms: 1 + -16 + 4x + 4x2 = 16 + -16 Combine like terms: 1 + -16 = -15 -15 + 4x + 4x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -15 + 4x + 4x2 = 0 Factor a trinomial. (-5 + -2x)(3 + -2x) = 0Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-2.5, 1.5}
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