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Simplifying (2x + -9)(2x + -9) + -1 = 0 Reorder the terms: (-9 + 2x)(2x + -9) + -1 = 0 Reorder the terms: (-9 + 2x)(-9 + 2x) + -1 = 0 Multiply (-9 + 2x) * (-9 + 2x) (-9(-9 + 2x) + 2x * (-9 + 2x)) + -1 = 0 ((-9 * -9 + 2x * -9) + 2x * (-9 + 2x)) + -1 = 0 ((81 + -18x) + 2x * (-9 + 2x)) + -1 = 0 (81 + -18x + (-9 * 2x + 2x * 2x)) + -1 = 0 (81 + -18x + (-18x + 4x2)) + -1 = 0 Combine like terms: -18x + -18x = -36x (81 + -36x + 4x2) + -1 = 0 Reorder the terms: 81 + -1 + -36x + 4x2 = 0 Combine like terms: 81 + -1 = 80 80 + -36x + 4x2 = 0 Solving 80 + -36x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(20 + -9x + x2) = 0 Factor a trinomial. 4((4 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
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 = 5Solution
x = {4, 5}
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