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Simplifying (20 + X)(8 + X) = 288 Multiply (20 + X) * (8 + X) (20(8 + X) + X(8 + X)) = 288 ((8 * 20 + X * 20) + X(8 + X)) = 288 ((160 + 20X) + X(8 + X)) = 288 (160 + 20X + (8 * X + X * X)) = 288 (160 + 20X + (8X + X2)) = 288 Combine like terms: 20X + 8X = 28X (160 + 28X + X2) = 288 Solving 160 + 28X + X2 = 288 Solving for variable 'X'. Reorder the terms: 160 + -288 + 28X + X2 = 288 + -288 Combine like terms: 160 + -288 = -128 -128 + 28X + X2 = 288 + -288 Combine like terms: 288 + -288 = 0 -128 + 28X + X2 = 0 Factor a trinomial. (-32 + -1X)(4 + -1X) = 0Subproblem 1
Set the factor '(-32 + -1X)' equal to zero and attempt to solve: Simplifying -32 + -1X = 0 Solving -32 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -1X = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -1X = 0 + 32 -1X = 0 + 32 Combine like terms: 0 + 32 = 32 -1X = 32 Divide each side by '-1'. X = -32 Simplifying X = -32Subproblem 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 = {-32, 4}
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