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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((-6 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 = -6Subproblem 2
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 = 3Solution
x = {-6, 3}
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