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Simplifying 0 = -10x2 + 3500x + -250000 Reorder the terms: 0 = -250000 + 3500x + -10x2 Solving 0 = -250000 + 3500x + -10x2 Solving for variable 'x'. Combine like terms: 0 + 250000 = 250000 250000 + -3500x + 10x2 = -250000 + 3500x + -10x2 + 250000 + -3500x + 10x2 Reorder the terms: 250000 + -3500x + 10x2 = -250000 + 250000 + 3500x + -3500x + -10x2 + 10x2 Combine like terms: -250000 + 250000 = 0 250000 + -3500x + 10x2 = 0 + 3500x + -3500x + -10x2 + 10x2 250000 + -3500x + 10x2 = 3500x + -3500x + -10x2 + 10x2 Combine like terms: 3500x + -3500x = 0 250000 + -3500x + 10x2 = 0 + -10x2 + 10x2 250000 + -3500x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 250000 + -3500x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(25000 + -350x + x2) = 0 Factor a trinomial. 10((100 + -1x)(250 + -1x)) = 0 Ignore the factor 10.Subproblem 1
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 = 100Subproblem 2
Set the factor '(250 + -1x)' equal to zero and attempt to solve: Simplifying 250 + -1x = 0 Solving 250 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + -1x = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -1x = 0 + -250 -1x = 0 + -250 Combine like terms: 0 + -250 = -250 -1x = -250 Divide each side by '-1'. x = 250 Simplifying x = 250Solution
x = {100, 250}
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