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Simplifying (72 + x)(48 + x) = 6912 Multiply (72 + x) * (48 + x) (72(48 + x) + x(48 + x)) = 6912 ((48 * 72 + x * 72) + x(48 + x)) = 6912 ((3456 + 72x) + x(48 + x)) = 6912 (3456 + 72x + (48 * x + x * x)) = 6912 (3456 + 72x + (48x + x2)) = 6912 Combine like terms: 72x + 48x = 120x (3456 + 120x + x2) = 6912 Solving 3456 + 120x + x2 = 6912 Solving for variable 'x'. Reorder the terms: 3456 + -6912 + 120x + x2 = 6912 + -6912 Combine like terms: 3456 + -6912 = -3456 -3456 + 120x + x2 = 6912 + -6912 Combine like terms: 6912 + -6912 = 0 -3456 + 120x + x2 = 0 Factor a trinomial. (-144 + -1x)(24 + -1x) = 0Subproblem 1
Set the factor '(-144 + -1x)' equal to zero and attempt to solve: Simplifying -144 + -1x = 0 Solving -144 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '144' to each side of the equation. -144 + 144 + -1x = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -1x = 0 + 144 -1x = 0 + 144 Combine like terms: 0 + 144 = 144 -1x = 144 Divide each side by '-1'. x = -144 Simplifying x = -144Subproblem 2
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 = 24Solution
x = {-144, 24}
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