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Simplifying (20 + 2x)(24 + 2x) = 1596 Multiply (20 + 2x) * (24 + 2x) (20(24 + 2x) + 2x * (24 + 2x)) = 1596 ((24 * 20 + 2x * 20) + 2x * (24 + 2x)) = 1596 ((480 + 40x) + 2x * (24 + 2x)) = 1596 (480 + 40x + (24 * 2x + 2x * 2x)) = 1596 (480 + 40x + (48x + 4x2)) = 1596 Combine like terms: 40x + 48x = 88x (480 + 88x + 4x2) = 1596 Solving 480 + 88x + 4x2 = 1596 Solving for variable 'x'. Reorder the terms: 480 + -1596 + 88x + 4x2 = 1596 + -1596 Combine like terms: 480 + -1596 = -1116 -1116 + 88x + 4x2 = 1596 + -1596 Combine like terms: 1596 + -1596 = 0 -1116 + 88x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-279 + 22x + x2) = 0 Factor a trinomial. 4((-31 + -1x)(9 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-31 + -1x)' equal to zero and attempt to solve: Simplifying -31 + -1x = 0 Solving -31 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + -1x = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -1x = 0 + 31 -1x = 0 + 31 Combine like terms: 0 + 31 = 31 -1x = 31 Divide each side by '-1'. x = -31 Simplifying x = -31Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-31, 9}
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