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Simplifying (15 + -1x)(20 + -1x) = 234 Multiply (15 + -1x) * (20 + -1x) (15(20 + -1x) + -1x * (20 + -1x)) = 234 ((20 * 15 + -1x * 15) + -1x * (20 + -1x)) = 234 ((300 + -15x) + -1x * (20 + -1x)) = 234 (300 + -15x + (20 * -1x + -1x * -1x)) = 234 (300 + -15x + (-20x + 1x2)) = 234 Combine like terms: -15x + -20x = -35x (300 + -35x + 1x2) = 234 Solving 300 + -35x + 1x2 = 234 Solving for variable 'x'. Reorder the terms: 300 + -234 + -35x + 1x2 = 234 + -234 Combine like terms: 300 + -234 = 66 66 + -35x + 1x2 = 234 + -234 Combine like terms: 234 + -234 = 0 66 + -35x + 1x2 = 0 Factor a trinomial. (2 + -1x)(33 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(33 + -1x)' equal to zero and attempt to solve: Simplifying 33 + -1x = 0 Solving 33 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + -1x = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -1x = 0 + -33 -1x = 0 + -33 Combine like terms: 0 + -33 = -33 -1x = -33 Divide each side by '-1'. x = 33 Simplifying x = 33Solution
x = {2, 33}
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