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Simplifying (2x + -1)(2x + -1) = 121 Reorder the terms: (-1 + 2x)(2x + -1) = 121 Reorder the terms: (-1 + 2x)(-1 + 2x) = 121 Multiply (-1 + 2x) * (-1 + 2x) (-1(-1 + 2x) + 2x * (-1 + 2x)) = 121 ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 121 ((1 + -2x) + 2x * (-1 + 2x)) = 121 (1 + -2x + (-1 * 2x + 2x * 2x)) = 121 (1 + -2x + (-2x + 4x2)) = 121 Combine like terms: -2x + -2x = -4x (1 + -4x + 4x2) = 121 Solving 1 + -4x + 4x2 = 121 Solving for variable 'x'. Reorder the terms: 1 + -121 + -4x + 4x2 = 121 + -121 Combine like terms: 1 + -121 = -120 -120 + -4x + 4x2 = 121 + -121 Combine like terms: 121 + -121 = 0 -120 + -4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-30 + -1x + x2) = 0 Factor a trinomial. 4((-5 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-5, 6}
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