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Simplifying (10 + -1x)(12 + -1x) = 35 Multiply (10 + -1x) * (12 + -1x) (10(12 + -1x) + -1x * (12 + -1x)) = 35 ((12 * 10 + -1x * 10) + -1x * (12 + -1x)) = 35 ((120 + -10x) + -1x * (12 + -1x)) = 35 (120 + -10x + (12 * -1x + -1x * -1x)) = 35 (120 + -10x + (-12x + 1x2)) = 35 Combine like terms: -10x + -12x = -22x (120 + -22x + 1x2) = 35 Solving 120 + -22x + 1x2 = 35 Solving for variable 'x'. Reorder the terms: 120 + -35 + -22x + 1x2 = 35 + -35 Combine like terms: 120 + -35 = 85 85 + -22x + 1x2 = 35 + -35 Combine like terms: 35 + -35 = 0 85 + -22x + 1x2 = 0 Factor a trinomial. (5 + -1x)(17 + -1x) = 0Subproblem 1
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 = 5Subproblem 2
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 = 17Solution
x = {5, 17}
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