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Simplifying (8 + x)(12 + x) = 192 Multiply (8 + x) * (12 + x) (8(12 + x) + x(12 + x)) = 192 ((12 * 8 + x * 8) + x(12 + x)) = 192 ((96 + 8x) + x(12 + x)) = 192 (96 + 8x + (12 * x + x * x)) = 192 (96 + 8x + (12x + x2)) = 192 Combine like terms: 8x + 12x = 20x (96 + 20x + x2) = 192 Solving 96 + 20x + x2 = 192 Solving for variable 'x'. Reorder the terms: 96 + -192 + 20x + x2 = 192 + -192 Combine like terms: 96 + -192 = -96 -96 + 20x + x2 = 192 + -192 Combine like terms: 192 + -192 = 0 -96 + 20x + x2 = 0 Factor a trinomial. (-24 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve: Simplifying -24 + -1x = 0 Solving -24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1x = 0 + 24 -1x = 0 + 24 Combine like terms: 0 + 24 = 24 -1x = 24 Divide each side by '-1'. x = -24 Simplifying x = -24Subproblem 2
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 = 4Solution
x = {-24, 4}
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