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Simplifying (x + -1)(x + 3) = 17 + x Reorder the terms: (-1 + x)(x + 3) = 17 + x Reorder the terms: (-1 + x)(3 + x) = 17 + x Multiply (-1 + x) * (3 + x) (-1(3 + x) + x(3 + x)) = 17 + x ((3 * -1 + x * -1) + x(3 + x)) = 17 + x ((-3 + -1x) + x(3 + x)) = 17 + x (-3 + -1x + (3 * x + x * x)) = 17 + x (-3 + -1x + (3x + x2)) = 17 + x Combine like terms: -1x + 3x = 2x (-3 + 2x + x2) = 17 + x Solving -3 + 2x + x2 = 17 + x Solving for variable 'x'. Reorder the terms: -3 + -17 + 2x + -1x + x2 = 17 + x + -17 + -1x Combine like terms: -3 + -17 = -20 -20 + 2x + -1x + x2 = 17 + x + -17 + -1x Combine like terms: 2x + -1x = 1x -20 + 1x + x2 = 17 + x + -17 + -1x Reorder the terms: -20 + 1x + x2 = 17 + -17 + x + -1x Combine like terms: 17 + -17 = 0 -20 + 1x + x2 = 0 + x + -1x -20 + 1x + x2 = x + -1x Combine like terms: x + -1x = 0 -20 + 1x + x2 = 0 Factor a trinomial. (-5 + -1x)(4 + -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 '(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 = 4Solution
x = {-5, 4}
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