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Simplifying (8 + -1x)(5 + -1x) = 40 + -12 Multiply (8 + -1x) * (5 + -1x) (8(5 + -1x) + -1x * (5 + -1x)) = 40 + -12 ((5 * 8 + -1x * 8) + -1x * (5 + -1x)) = 40 + -12 ((40 + -8x) + -1x * (5 + -1x)) = 40 + -12 (40 + -8x + (5 * -1x + -1x * -1x)) = 40 + -12 (40 + -8x + (-5x + 1x2)) = 40 + -12 Combine like terms: -8x + -5x = -13x (40 + -13x + 1x2) = 40 + -12 Combine like terms: 40 + -12 = 28 40 + -13x + 1x2 = 28 Solving 40 + -13x + 1x2 = 28 Solving for variable 'x'. Reorder the terms: 40 + -28 + -13x + 1x2 = 28 + -28 Combine like terms: 40 + -28 = 12 12 + -13x + 1x2 = 28 + -28 Combine like terms: 28 + -28 = 0 12 + -13x + 1x2 = 0 Factor a trinomial. (1 + -1x)(12 + -1x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {1, 12}
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