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Simplifying (17 + x)(13 + x) = 396 Multiply (17 + x) * (13 + x) (17(13 + x) + x(13 + x)) = 396 ((13 * 17 + x * 17) + x(13 + x)) = 396 ((221 + 17x) + x(13 + x)) = 396 (221 + 17x + (13 * x + x * x)) = 396 (221 + 17x + (13x + x2)) = 396 Combine like terms: 17x + 13x = 30x (221 + 30x + x2) = 396 Solving 221 + 30x + x2 = 396 Solving for variable 'x'. Reorder the terms: 221 + -396 + 30x + x2 = 396 + -396 Combine like terms: 221 + -396 = -175 -175 + 30x + x2 = 396 + -396 Combine like terms: 396 + -396 = 0 -175 + 30x + x2 = 0 Factor a trinomial. (-35 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-35 + -1x)' equal to zero and attempt to solve: Simplifying -35 + -1x = 0 Solving -35 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + -1x = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -1x = 0 + 35 -1x = 0 + 35 Combine like terms: 0 + 35 = 35 -1x = 35 Divide each side by '-1'. x = -35 Simplifying x = -35Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-35, 5}
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