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Simplifying 2x2 + -9x + -65 = x2 + -1x Reorder the terms: -65 + -9x + 2x2 = x2 + -1x Reorder the terms: -65 + -9x + 2x2 = -1x + x2 Solving -65 + -9x + 2x2 = -1x + x2 Solving for variable 'x'. Reorder the terms: -65 + -9x + x + 2x2 + -1x2 = -1x + x2 + x + -1x2 Combine like terms: -9x + x = -8x -65 + -8x + 2x2 + -1x2 = -1x + x2 + x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -65 + -8x + 1x2 = -1x + x2 + x + -1x2 Reorder the terms: -65 + -8x + 1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 -65 + -8x + 1x2 = 0 + x2 + -1x2 -65 + -8x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -65 + -8x + 1x2 = 0 Factor a trinomial. (-5 + -1x)(13 + -1x) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 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 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-5, 13}
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