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Simplifying (6 + x)(9 + x) = 88 Multiply (6 + x) * (9 + x) (6(9 + x) + x(9 + x)) = 88 ((9 * 6 + x * 6) + x(9 + x)) = 88 ((54 + 6x) + x(9 + x)) = 88 (54 + 6x + (9 * x + x * x)) = 88 (54 + 6x + (9x + x2)) = 88 Combine like terms: 6x + 9x = 15x (54 + 15x + x2) = 88 Solving 54 + 15x + x2 = 88 Solving for variable 'x'. Reorder the terms: 54 + -88 + 15x + x2 = 88 + -88 Combine like terms: 54 + -88 = -34 -34 + 15x + x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -34 + 15x + x2 = 0 Factor a trinomial. (-17 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-17, 2}
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