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Simplifying (2x + 1)(2x + 1) = 4 Reorder the terms: (1 + 2x)(2x + 1) = 4 Reorder the terms: (1 + 2x)(1 + 2x) = 4 Multiply (1 + 2x) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x)) = 4 ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 4 ((1 + 2x) + 2x * (1 + 2x)) = 4 (1 + 2x + (1 * 2x + 2x * 2x)) = 4 (1 + 2x + (2x + 4x2)) = 4 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2) = 4 Solving 1 + 4x + 4x2 = 4 Solving for variable 'x'. Reorder the terms: 1 + -4 + 4x + 4x2 = 4 + -4 Combine like terms: 1 + -4 = -3 -3 + 4x + 4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -3 + 4x + 4x2 = 0 Factor a trinomial. (-3 + -2x)(1 + -2x) = 0Subproblem 1
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 = -1.5Subproblem 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 = {-1.5, 0.5}
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