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Simplifying 288 = (16 + 2x)(8 + x) Multiply (16 + 2x) * (8 + x) 288 = (16(8 + x) + 2x * (8 + x)) 288 = ((8 * 16 + x * 16) + 2x * (8 + x)) 288 = ((128 + 16x) + 2x * (8 + x)) 288 = (128 + 16x + (8 * 2x + x * 2x)) 288 = (128 + 16x + (16x + 2x2)) Combine like terms: 16x + 16x = 32x 288 = (128 + 32x + 2x2) Solving 288 = 128 + 32x + 2x2 Solving for variable 'x'. Combine like terms: 288 + -128 = 160 160 + -32x + -2x2 = 128 + 32x + 2x2 + -128 + -32x + -2x2 Reorder the terms: 160 + -32x + -2x2 = 128 + -128 + 32x + -32x + 2x2 + -2x2 Combine like terms: 128 + -128 = 0 160 + -32x + -2x2 = 0 + 32x + -32x + 2x2 + -2x2 160 + -32x + -2x2 = 32x + -32x + 2x2 + -2x2 Combine like terms: 32x + -32x = 0 160 + -32x + -2x2 = 0 + 2x2 + -2x2 160 + -32x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 160 + -32x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(80 + -16x + -1x2) = 0 Factor a trinomial. 2((4 + -1x)(20 + x)) = 0 Ignore the factor 2.Subproblem 1
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 = 4Subproblem 2
Set the factor '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20Solution
x = {4, -20}
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