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Simplifying (2 + x)(12 + x) = 75 Multiply (2 + x) * (12 + x) (2(12 + x) + x(12 + x)) = 75 ((12 * 2 + x * 2) + x(12 + x)) = 75 ((24 + 2x) + x(12 + x)) = 75 (24 + 2x + (12 * x + x * x)) = 75 (24 + 2x + (12x + x2)) = 75 Combine like terms: 2x + 12x = 14x (24 + 14x + x2) = 75 Solving 24 + 14x + x2 = 75 Solving for variable 'x'. Reorder the terms: 24 + -75 + 14x + x2 = 75 + -75 Combine like terms: 24 + -75 = -51 -51 + 14x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -51 + 14x + x2 = 0 Factor a trinomial. (-17 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve: Simplifying -17 + -1x = 0 Solving -17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x = 0 + 17 -1x = 0 + 17 Combine like terms: 0 + 17 = 17 -1x = 17 Divide each side by '-1'. x = -17 Simplifying x = -17Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-17, 3}
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