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Simplifying (2x + -9)(2x + -8) = 0 Reorder the terms: (-9 + 2x)(2x + -8) = 0 Reorder the terms: (-9 + 2x)(-8 + 2x) = 0 Multiply (-9 + 2x) * (-8 + 2x) (-9(-8 + 2x) + 2x * (-8 + 2x)) = 0 ((-8 * -9 + 2x * -9) + 2x * (-8 + 2x)) = 0 ((72 + -18x) + 2x * (-8 + 2x)) = 0 (72 + -18x + (-8 * 2x + 2x * 2x)) = 0 (72 + -18x + (-16x + 4x2)) = 0 Combine like terms: -18x + -16x = -34x (72 + -34x + 4x2) = 0 Solving 72 + -34x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -17x + 2x2) = 0 Factor a trinomial. 2((4 + -1x)(9 + -2x)) = 0 Ignore the factor 2.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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {4, 4.5}
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