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Simplifying (2x + -3)(2x + -3) = 81 Reorder the terms: (-3 + 2x)(2x + -3) = 81 Reorder the terms: (-3 + 2x)(-3 + 2x) = 81 Multiply (-3 + 2x) * (-3 + 2x) (-3(-3 + 2x) + 2x * (-3 + 2x)) = 81 ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 81 ((9 + -6x) + 2x * (-3 + 2x)) = 81 (9 + -6x + (-3 * 2x + 2x * 2x)) = 81 (9 + -6x + (-6x + 4x2)) = 81 Combine like terms: -6x + -6x = -12x (9 + -12x + 4x2) = 81 Solving 9 + -12x + 4x2 = 81 Solving for variable 'x'. Reorder the terms: 9 + -81 + -12x + 4x2 = 81 + -81 Combine like terms: 9 + -81 = -72 -72 + -12x + 4x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -72 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + -3x + x2) = 0 Factor a trinomial. 4((-3 + -1x)(6 + -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 '(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 = {-3, 6}
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