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Simplifying 9000 = (30 + 2x)(350 + -25x) Multiply (30 + 2x) * (350 + -25x) 9000 = (30(350 + -25x) + 2x * (350 + -25x)) 9000 = ((350 * 30 + -25x * 30) + 2x * (350 + -25x)) 9000 = ((10500 + -750x) + 2x * (350 + -25x)) 9000 = (10500 + -750x + (350 * 2x + -25x * 2x)) 9000 = (10500 + -750x + (700x + -50x2)) Combine like terms: -750x + 700x = -50x 9000 = (10500 + -50x + -50x2) Solving 9000 = 10500 + -50x + -50x2 Solving for variable 'x'. Combine like terms: 9000 + -10500 = -1500 -1500 + 50x + 50x2 = 10500 + -50x + -50x2 + -10500 + 50x + 50x2 Reorder the terms: -1500 + 50x + 50x2 = 10500 + -10500 + -50x + 50x + -50x2 + 50x2 Combine like terms: 10500 + -10500 = 0 -1500 + 50x + 50x2 = 0 + -50x + 50x + -50x2 + 50x2 -1500 + 50x + 50x2 = -50x + 50x + -50x2 + 50x2 Combine like terms: -50x + 50x = 0 -1500 + 50x + 50x2 = 0 + -50x2 + 50x2 -1500 + 50x + 50x2 = -50x2 + 50x2 Combine like terms: -50x2 + 50x2 = 0 -1500 + 50x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-30 + x + x2) = 0 Factor a trinomial. 50((-6 + -1x)(5 + -1x)) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-6, 5}
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