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Simplifying (12 + x)(7 + x) = 234 Multiply (12 + x) * (7 + x) (12(7 + x) + x(7 + x)) = 234 ((7 * 12 + x * 12) + x(7 + x)) = 234 ((84 + 12x) + x(7 + x)) = 234 (84 + 12x + (7 * x + x * x)) = 234 (84 + 12x + (7x + x2)) = 234 Combine like terms: 12x + 7x = 19x (84 + 19x + x2) = 234 Solving 84 + 19x + x2 = 234 Solving for variable 'x'. Reorder the terms: 84 + -234 + 19x + x2 = 234 + -234 Combine like terms: 84 + -234 = -150 -150 + 19x + x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -150 + 19x + x2 = 0 Factor a trinomial. (-25 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-25 + -1x)' equal to zero and attempt to solve: Simplifying -25 + -1x = 0 Solving -25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1x = 0 + 25 -1x = 0 + 25 Combine like terms: 0 + 25 = 25 -1x = 25 Divide each side by '-1'. x = -25 Simplifying x = -25Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-25, 6}
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