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Simplifying (24 + 2x)(16 + 2x) = 2(24)(16) Multiply (24 + 2x) * (16 + 2x) (24(16 + 2x) + 2x * (16 + 2x)) = 2(24)(16) ((16 * 24 + 2x * 24) + 2x * (16 + 2x)) = 2(24)(16) ((384 + 48x) + 2x * (16 + 2x)) = 2(24)(16) (384 + 48x + (16 * 2x + 2x * 2x)) = 2(24)(16) (384 + 48x + (32x + 4x2)) = 2(24)(16) Combine like terms: 48x + 32x = 80x (384 + 80x + 4x2) = 2(24)(16) Multiply 2 * 24 384 + 80x + 4x2 = 48 * 16 Multiply 48 * 16 384 + 80x + 4x2 = 768 Solving 384 + 80x + 4x2 = 768 Solving for variable 'x'. Reorder the terms: 384 + -768 + 80x + 4x2 = 768 + -768 Combine like terms: 384 + -768 = -384 -384 + 80x + 4x2 = 768 + -768 Combine like terms: 768 + -768 = 0 -384 + 80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-96 + 20x + x2) = 0 Factor a trinomial. 4((-24 + -1x)(4 + -1x)) = 0 Ignore the factor 4.Subproblem 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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