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Simplifying (2x + 24)(2x + 16) = 660 Reorder the terms: (24 + 2x)(2x + 16) = 660 Reorder the terms: (24 + 2x)(16 + 2x) = 660 Multiply (24 + 2x) * (16 + 2x) (24(16 + 2x) + 2x * (16 + 2x)) = 660 ((16 * 24 + 2x * 24) + 2x * (16 + 2x)) = 660 ((384 + 48x) + 2x * (16 + 2x)) = 660 (384 + 48x + (16 * 2x + 2x * 2x)) = 660 (384 + 48x + (32x + 4x2)) = 660 Combine like terms: 48x + 32x = 80x (384 + 80x + 4x2) = 660 Solving 384 + 80x + 4x2 = 660 Solving for variable 'x'. Reorder the terms: 384 + -660 + 80x + 4x2 = 660 + -660 Combine like terms: 384 + -660 = -276 -276 + 80x + 4x2 = 660 + -660 Combine like terms: 660 + -660 = 0 -276 + 80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-69 + 20x + x2) = 0 Factor a trinomial. 4((-23 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve: Simplifying -23 + -1x = 0 Solving -23 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1x = 0 + 23 -1x = 0 + 23 Combine like terms: 0 + 23 = 23 -1x = 23 Divide each side by '-1'. x = -23 Simplifying x = -23Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-23, 3}
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