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Simplifying (12 + -1x)(7 + -1x) = 50 Multiply (12 + -1x) * (7 + -1x) (12(7 + -1x) + -1x * (7 + -1x)) = 50 ((7 * 12 + -1x * 12) + -1x * (7 + -1x)) = 50 ((84 + -12x) + -1x * (7 + -1x)) = 50 (84 + -12x + (7 * -1x + -1x * -1x)) = 50 (84 + -12x + (-7x + 1x2)) = 50 Combine like terms: -12x + -7x = -19x (84 + -19x + 1x2) = 50 Solving 84 + -19x + 1x2 = 50 Solving for variable 'x'. Reorder the terms: 84 + -50 + -19x + 1x2 = 50 + -50 Combine like terms: 84 + -50 = 34 34 + -19x + 1x2 = 50 + -50 Combine like terms: 50 + -50 = 0 34 + -19x + 1x2 = 0 Factor a trinomial. (2 + -1x)(17 + -1x) = 0Subproblem 1
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 = 2Subproblem 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 = {2, 17}
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