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Simplifying (18 + -1x)(12 + -1x) = 112 Multiply (18 + -1x) * (12 + -1x) (18(12 + -1x) + -1x * (12 + -1x)) = 112 ((12 * 18 + -1x * 18) + -1x * (12 + -1x)) = 112 ((216 + -18x) + -1x * (12 + -1x)) = 112 (216 + -18x + (12 * -1x + -1x * -1x)) = 112 (216 + -18x + (-12x + 1x2)) = 112 Combine like terms: -18x + -12x = -30x (216 + -30x + 1x2) = 112 Solving 216 + -30x + 1x2 = 112 Solving for variable 'x'. Reorder the terms: 216 + -112 + -30x + 1x2 = 112 + -112 Combine like terms: 216 + -112 = 104 104 + -30x + 1x2 = 112 + -112 Combine like terms: 112 + -112 = 0 104 + -30x + 1x2 = 0 Factor a trinomial. (4 + -1x)(26 + -1x) = 0Subproblem 1
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 = 4Subproblem 2
Set the factor '(26 + -1x)' equal to zero and attempt to solve: Simplifying 26 + -1x = 0 Solving 26 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + -1x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -1x = 0 + -26 -1x = 0 + -26 Combine like terms: 0 + -26 = -26 -1x = -26 Divide each side by '-1'. x = 26 Simplifying x = 26Solution
x = {4, 26}
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