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Simplifying (2x + 9)(x + -5) = 108 Reorder the terms: (9 + 2x)(x + -5) = 108 Reorder the terms: (9 + 2x)(-5 + x) = 108 Multiply (9 + 2x) * (-5 + x) (9(-5 + x) + 2x * (-5 + x)) = 108 ((-5 * 9 + x * 9) + 2x * (-5 + x)) = 108 ((-45 + 9x) + 2x * (-5 + x)) = 108 (-45 + 9x + (-5 * 2x + x * 2x)) = 108 (-45 + 9x + (-10x + 2x2)) = 108 Combine like terms: 9x + -10x = -1x (-45 + -1x + 2x2) = 108 Solving -45 + -1x + 2x2 = 108 Solving for variable 'x'. Reorder the terms: -45 + -108 + -1x + 2x2 = 108 + -108 Combine like terms: -45 + -108 = -153 -153 + -1x + 2x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -153 + -1x + 2x2 = 0 Factor a trinomial. (-17 + -2x)(9 + -1x) = 0Subproblem 1
Set the factor '(-17 + -2x)' equal to zero and attempt to solve: Simplifying -17 + -2x = 0 Solving -17 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -2x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2x = 0 + 17 -2x = 0 + 17 Combine like terms: 0 + 17 = 17 -2x = 17 Divide each side by '-2'. x = -8.5 Simplifying x = -8.5Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-8.5, 9}
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