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Simplifying (12 + x)(16 + x) = 525 Multiply (12 + x) * (16 + x) (12(16 + x) + x(16 + x)) = 525 ((16 * 12 + x * 12) + x(16 + x)) = 525 ((192 + 12x) + x(16 + x)) = 525 (192 + 12x + (16 * x + x * x)) = 525 (192 + 12x + (16x + x2)) = 525 Combine like terms: 12x + 16x = 28x (192 + 28x + x2) = 525 Solving 192 + 28x + x2 = 525 Solving for variable 'x'. Reorder the terms: 192 + -525 + 28x + x2 = 525 + -525 Combine like terms: 192 + -525 = -333 -333 + 28x + x2 = 525 + -525 Combine like terms: 525 + -525 = 0 -333 + 28x + x2 = 0 Factor a trinomial. (-37 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(-37 + -1x)' equal to zero and attempt to solve: Simplifying -37 + -1x = 0 Solving -37 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + -1x = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -1x = 0 + 37 -1x = 0 + 37 Combine like terms: 0 + 37 = 37 -1x = 37 Divide each side by '-1'. x = -37 Simplifying x = -37Subproblem 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 = {-37, 9}
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