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Simplifying 8000 = -5x2 + 450x + -1000 Reorder the terms: 8000 = -1000 + 450x + -5x2 Solving 8000 = -1000 + 450x + -5x2 Solving for variable 'x'. Combine like terms: 8000 + 1000 = 9000 9000 + -450x + 5x2 = -1000 + 450x + -5x2 + 1000 + -450x + 5x2 Reorder the terms: 9000 + -450x + 5x2 = -1000 + 1000 + 450x + -450x + -5x2 + 5x2 Combine like terms: -1000 + 1000 = 0 9000 + -450x + 5x2 = 0 + 450x + -450x + -5x2 + 5x2 9000 + -450x + 5x2 = 450x + -450x + -5x2 + 5x2 Combine like terms: 450x + -450x = 0 9000 + -450x + 5x2 = 0 + -5x2 + 5x2 9000 + -450x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 9000 + -450x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1800 + -90x + x2) = 0 Factor a trinomial. 5((30 + -1x)(60 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Solution
x = {30, 60}
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