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Simplifying (5 + -1x)(10 + -1x) = 36 Multiply (5 + -1x) * (10 + -1x) (5(10 + -1x) + -1x * (10 + -1x)) = 36 ((10 * 5 + -1x * 5) + -1x * (10 + -1x)) = 36 ((50 + -5x) + -1x * (10 + -1x)) = 36 (50 + -5x + (10 * -1x + -1x * -1x)) = 36 (50 + -5x + (-10x + 1x2)) = 36 Combine like terms: -5x + -10x = -15x (50 + -15x + 1x2) = 36 Solving 50 + -15x + 1x2 = 36 Solving for variable 'x'. Reorder the terms: 50 + -36 + -15x + 1x2 = 36 + -36 Combine like terms: 50 + -36 = 14 14 + -15x + 1x2 = 36 + -36 Combine like terms: 36 + -36 = 0 14 + -15x + 1x2 = 0 Factor a trinomial. (1 + -1x)(14 + -1x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {1, 14}
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