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Simplifying (12 + x)(16 + x) = 285 Multiply (12 + x) * (16 + x) (12(16 + x) + x(16 + x)) = 285 ((16 * 12 + x * 12) + x(16 + x)) = 285 ((192 + 12x) + x(16 + x)) = 285 (192 + 12x + (16 * x + x * x)) = 285 (192 + 12x + (16x + x2)) = 285 Combine like terms: 12x + 16x = 28x (192 + 28x + x2) = 285 Solving 192 + 28x + x2 = 285 Solving for variable 'x'. Reorder the terms: 192 + -285 + 28x + x2 = 285 + -285 Combine like terms: 192 + -285 = -93 -93 + 28x + x2 = 285 + -285 Combine like terms: 285 + -285 = 0 -93 + 28x + x2 = 0 Factor a trinomial. (-31 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-31 + -1x)' equal to zero and attempt to solve: Simplifying -31 + -1x = 0 Solving -31 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + -1x = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -1x = 0 + 31 -1x = 0 + 31 Combine like terms: 0 + 31 = 31 -1x = 31 Divide each side by '-1'. x = -31 Simplifying x = -31Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-31, 3}
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