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Simplifying (2x + 1)(2x + 1) + -25 = 0 Reorder the terms: (1 + 2x)(2x + 1) + -25 = 0 Reorder the terms: (1 + 2x)(1 + 2x) + -25 = 0 Multiply (1 + 2x) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x)) + -25 = 0 ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -25 = 0 ((1 + 2x) + 2x * (1 + 2x)) + -25 = 0 (1 + 2x + (1 * 2x + 2x * 2x)) + -25 = 0 (1 + 2x + (2x + 4x2)) + -25 = 0 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2) + -25 = 0 Reorder the terms: 1 + -25 + 4x + 4x2 = 0 Combine like terms: 1 + -25 = -24 -24 + 4x + 4x2 = 0 Solving -24 + 4x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + x + x2) = 0 Factor a trinomial. 4((-3 + -1x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
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 = 2Solution
x = {-3, 2}
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