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Simplifying (10000 + -10x)(300 + -1x) = 0 Multiply (10000 + -10x) * (300 + -1x) (10000(300 + -1x) + -10x * (300 + -1x)) = 0 ((300 * 10000 + -1x * 10000) + -10x * (300 + -1x)) = 0 ((3000000 + -10000x) + -10x * (300 + -1x)) = 0 (3000000 + -10000x + (300 * -10x + -1x * -10x)) = 0 (3000000 + -10000x + (-3000x + 10x2)) = 0 Combine like terms: -10000x + -3000x = -13000x (3000000 + -13000x + 10x2) = 0 Solving 3000000 + -13000x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(300000 + -1300x + x2) = 0 Factor a trinomial. 10((300 + -1x)(1000 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(300 + -1x)' equal to zero and attempt to solve: Simplifying 300 + -1x = 0 Solving 300 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + -1x = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -1x = 0 + -300 -1x = 0 + -300 Combine like terms: 0 + -300 = -300 -1x = -300 Divide each side by '-1'. x = 300 Simplifying x = 300Subproblem 2
Set the factor '(1000 + -1x)' equal to zero and attempt to solve: Simplifying 1000 + -1x = 0 Solving 1000 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1000' to each side of the equation. 1000 + -1000 + -1x = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -1x = 0 + -1000 -1x = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -1x = -1000 Divide each side by '-1'. x = 1000 Simplifying x = 1000Solution
x = {300, 1000}
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