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Simplifying (200 + x)(300 + x) = 120000 Multiply (200 + x) * (300 + x) (200(300 + x) + x(300 + x)) = 120000 ((300 * 200 + x * 200) + x(300 + x)) = 120000 ((60000 + 200x) + x(300 + x)) = 120000 (60000 + 200x + (300 * x + x * x)) = 120000 (60000 + 200x + (300x + x2)) = 120000 Combine like terms: 200x + 300x = 500x (60000 + 500x + x2) = 120000 Solving 60000 + 500x + x2 = 120000 Solving for variable 'x'. Reorder the terms: 60000 + -120000 + 500x + x2 = 120000 + -120000 Combine like terms: 60000 + -120000 = -60000 -60000 + 500x + x2 = 120000 + -120000 Combine like terms: 120000 + -120000 = 0 -60000 + 500x + x2 = 0 Factor a trinomial. (-600 + -1x)(100 + -1x) = 0Subproblem 1
Set the factor '(-600 + -1x)' equal to zero and attempt to solve: Simplifying -600 + -1x = 0 Solving -600 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '600' to each side of the equation. -600 + 600 + -1x = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -1x = 0 + 600 -1x = 0 + 600 Combine like terms: 0 + 600 = 600 -1x = 600 Divide each side by '-1'. x = -600 Simplifying x = -600Subproblem 2
Set the factor '(100 + -1x)' equal to zero and attempt to solve: Simplifying 100 + -1x = 0 Solving 100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1x = 0 + -100 -1x = 0 + -100 Combine like terms: 0 + -100 = -100 -1x = -100 Divide each side by '-1'. x = 100 Simplifying x = 100Solution
x = {-600, 100}
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