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Simplifying 117 = x(2x + -5) Reorder the terms: 117 = x(-5 + 2x) 117 = (-5 * x + 2x * x) 117 = (-5x + 2x2) Solving 117 = -5x + 2x2 Solving for variable 'x'. Reorder the terms: 117 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 117 + 5x + -2x2 = 0 + 2x2 + -2x2 117 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 117 + 5x + -2x2 = 0 Factor a trinomial. (9 + -1x)(13 + 2x) = 0Subproblem 1
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 = 9Subproblem 2
Set the factor '(13 + 2x)' equal to zero and attempt to solve: Simplifying 13 + 2x = 0 Solving 13 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2x = 0 + -13 2x = 0 + -13 Combine like terms: 0 + -13 = -13 2x = -13 Divide each side by '2'. x = -6.5 Simplifying x = -6.5Solution
x = {9, -6.5}
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