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Simplifying (50 + X)(10 + X) = 1200 Multiply (50 + X) * (10 + X) (50(10 + X) + X(10 + X)) = 1200 ((10 * 50 + X * 50) + X(10 + X)) = 1200 ((500 + 50X) + X(10 + X)) = 1200 (500 + 50X + (10 * X + X * X)) = 1200 (500 + 50X + (10X + X2)) = 1200 Combine like terms: 50X + 10X = 60X (500 + 60X + X2) = 1200 Solving 500 + 60X + X2 = 1200 Solving for variable 'X'. Reorder the terms: 500 + -1200 + 60X + X2 = 1200 + -1200 Combine like terms: 500 + -1200 = -700 -700 + 60X + X2 = 1200 + -1200 Combine like terms: 1200 + -1200 = 0 -700 + 60X + X2 = 0 Factor a trinomial. (-70 + -1X)(10 + -1X) = 0Subproblem 1
Set the factor '(-70 + -1X)' equal to zero and attempt to solve: Simplifying -70 + -1X = 0 Solving -70 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + -1X = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -1X = 0 + 70 -1X = 0 + 70 Combine like terms: 0 + 70 = 70 -1X = 70 Divide each side by '-1'. X = -70 Simplifying X = -70Subproblem 2
Set the factor '(10 + -1X)' equal to zero and attempt to solve: Simplifying 10 + -1X = 0 Solving 10 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1X = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1X = 0 + -10 -1X = 0 + -10 Combine like terms: 0 + -10 = -10 -1X = -10 Divide each side by '-1'. X = 10 Simplifying X = 10Solution
X = {-70, 10}
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