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Simplifying (2x + -5)(-1x + -1) = (-1x + -1)(x + 8) Reorder the terms: (-5 + 2x)(-1x + -1) = (-1x + -1)(x + 8) Reorder the terms: (-5 + 2x)(-1 + -1x) = (-1x + -1)(x + 8) Multiply (-5 + 2x) * (-1 + -1x) (-5(-1 + -1x) + 2x * (-1 + -1x)) = (-1x + -1)(x + 8) ((-1 * -5 + -1x * -5) + 2x * (-1 + -1x)) = (-1x + -1)(x + 8) ((5 + 5x) + 2x * (-1 + -1x)) = (-1x + -1)(x + 8) (5 + 5x + (-1 * 2x + -1x * 2x)) = (-1x + -1)(x + 8) (5 + 5x + (-2x + -2x2)) = (-1x + -1)(x + 8) Combine like terms: 5x + -2x = 3x (5 + 3x + -2x2) = (-1x + -1)(x + 8) Reorder the terms: 5 + 3x + -2x2 = (-1 + -1x)(x + 8) Reorder the terms: 5 + 3x + -2x2 = (-1 + -1x)(8 + x) Multiply (-1 + -1x) * (8 + x) 5 + 3x + -2x2 = (-1(8 + x) + -1x * (8 + x)) 5 + 3x + -2x2 = ((8 * -1 + x * -1) + -1x * (8 + x)) 5 + 3x + -2x2 = ((-8 + -1x) + -1x * (8 + x)) 5 + 3x + -2x2 = (-8 + -1x + (8 * -1x + x * -1x)) 5 + 3x + -2x2 = (-8 + -1x + (-8x + -1x2)) Combine like terms: -1x + -8x = -9x 5 + 3x + -2x2 = (-8 + -9x + -1x2) Solving 5 + 3x + -2x2 = -8 + -9x + -1x2 Solving for variable 'x'. Reorder the terms: 5 + 8 + 3x + 9x + -2x2 + x2 = -8 + -9x + -1x2 + 8 + 9x + x2 Combine like terms: 5 + 8 = 13 13 + 3x + 9x + -2x2 + x2 = -8 + -9x + -1x2 + 8 + 9x + x2 Combine like terms: 3x + 9x = 12x 13 + 12x + -2x2 + x2 = -8 + -9x + -1x2 + 8 + 9x + x2 Combine like terms: -2x2 + x2 = -1x2 13 + 12x + -1x2 = -8 + -9x + -1x2 + 8 + 9x + x2 Reorder the terms: 13 + 12x + -1x2 = -8 + 8 + -9x + 9x + -1x2 + x2 Combine like terms: -8 + 8 = 0 13 + 12x + -1x2 = 0 + -9x + 9x + -1x2 + x2 13 + 12x + -1x2 = -9x + 9x + -1x2 + x2 Combine like terms: -9x + 9x = 0 13 + 12x + -1x2 = 0 + -1x2 + x2 13 + 12x + -1x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 13 + 12x + -1x2 = 0 Factor a trinomial. (13 + -1x)(1 + x) = 0Subproblem 1
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 = 13Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {13, -1}
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