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Simplifying (24 + 2x)(16 + 2x) = 384 Multiply (24 + 2x) * (16 + 2x) (24(16 + 2x) + 2x * (16 + 2x)) = 384 ((16 * 24 + 2x * 24) + 2x * (16 + 2x)) = 384 ((384 + 48x) + 2x * (16 + 2x)) = 384 (384 + 48x + (16 * 2x + 2x * 2x)) = 384 (384 + 48x + (32x + 4x2)) = 384 Combine like terms: 48x + 32x = 80x (384 + 80x + 4x2) = 384 Add '-384' to each side of the equation. 384 + 80x + -384 + 4x2 = 384 + -384 Reorder the terms: 384 + -384 + 80x + 4x2 = 384 + -384 Combine like terms: 384 + -384 = 0 0 + 80x + 4x2 = 384 + -384 80x + 4x2 = 384 + -384 Combine like terms: 384 + -384 = 0 80x + 4x2 = 0 Solving 80x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(20 + x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = {0, -20}
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