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Simplifying (8 + x)(6 + -1x) = 13 Multiply (8 + x) * (6 + -1x) (8(6 + -1x) + x(6 + -1x)) = 13 ((6 * 8 + -1x * 8) + x(6 + -1x)) = 13 ((48 + -8x) + x(6 + -1x)) = 13 (48 + -8x + (6 * x + -1x * x)) = 13 (48 + -8x + (6x + -1x2)) = 13 Combine like terms: -8x + 6x = -2x (48 + -2x + -1x2) = 13 Solving 48 + -2x + -1x2 = 13 Solving for variable 'x'. Reorder the terms: 48 + -13 + -2x + -1x2 = 13 + -13 Combine like terms: 48 + -13 = 35 35 + -2x + -1x2 = 13 + -13 Combine like terms: 13 + -13 = 0 35 + -2x + -1x2 = 0 Factor a trinomial. (5 + -1x)(7 + x) = 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {5, -7}
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