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Simplifying (20 + x)(30 + x) = 936 Multiply (20 + x) * (30 + x) (20(30 + x) + x(30 + x)) = 936 ((30 * 20 + x * 20) + x(30 + x)) = 936 ((600 + 20x) + x(30 + x)) = 936 (600 + 20x + (30 * x + x * x)) = 936 (600 + 20x + (30x + x2)) = 936 Combine like terms: 20x + 30x = 50x (600 + 50x + x2) = 936 Solving 600 + 50x + x2 = 936 Solving for variable 'x'. Reorder the terms: 600 + -936 + 50x + x2 = 936 + -936 Combine like terms: 600 + -936 = -336 -336 + 50x + x2 = 936 + -936 Combine like terms: 936 + -936 = 0 -336 + 50x + x2 = 0 Factor a trinomial. (-56 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-56 + -1x)' equal to zero and attempt to solve: Simplifying -56 + -1x = 0 Solving -56 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + -1x = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -1x = 0 + 56 -1x = 0 + 56 Combine like terms: 0 + 56 = 56 -1x = 56 Divide each side by '-1'. x = -56 Simplifying x = -56Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-56, 6}
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