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Simplifying 0 = -10x2 + 3500x + -66000 Reorder the terms: 0 = -66000 + 3500x + -10x2 Solving 0 = -66000 + 3500x + -10x2 Solving for variable 'x'. Combine like terms: 0 + 66000 = 66000 66000 + -3500x + 10x2 = -66000 + 3500x + -10x2 + 66000 + -3500x + 10x2 Reorder the terms: 66000 + -3500x + 10x2 = -66000 + 66000 + 3500x + -3500x + -10x2 + 10x2 Combine like terms: -66000 + 66000 = 0 66000 + -3500x + 10x2 = 0 + 3500x + -3500x + -10x2 + 10x2 66000 + -3500x + 10x2 = 3500x + -3500x + -10x2 + 10x2 Combine like terms: 3500x + -3500x = 0 66000 + -3500x + 10x2 = 0 + -10x2 + 10x2 66000 + -3500x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 66000 + -3500x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(6600 + -350x + x2) = 0 Factor a trinomial. 10((20 + -1x)(330 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Subproblem 2
Set the factor '(330 + -1x)' equal to zero and attempt to solve: Simplifying 330 + -1x = 0 Solving 330 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-330' to each side of the equation. 330 + -330 + -1x = 0 + -330 Combine like terms: 330 + -330 = 0 0 + -1x = 0 + -330 -1x = 0 + -330 Combine like terms: 0 + -330 = -330 -1x = -330 Divide each side by '-1'. x = 330 Simplifying x = 330Solution
x = {20, 330}
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