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Simplifying 0 = 8x2 + -40x + -6000 Reorder the terms: 0 = -6000 + -40x + 8x2 Solving 0 = -6000 + -40x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 6000 = 6000 6000 + 40x + -8x2 = -6000 + -40x + 8x2 + 6000 + 40x + -8x2 Reorder the terms: 6000 + 40x + -8x2 = -6000 + 6000 + -40x + 40x + 8x2 + -8x2 Combine like terms: -6000 + 6000 = 0 6000 + 40x + -8x2 = 0 + -40x + 40x + 8x2 + -8x2 6000 + 40x + -8x2 = -40x + 40x + 8x2 + -8x2 Combine like terms: -40x + 40x = 0 6000 + 40x + -8x2 = 0 + 8x2 + -8x2 6000 + 40x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 6000 + 40x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(750 + 5x + -1x2) = 0 Factor a trinomial. 8((30 + -1x)(25 + x)) = 0 Ignore the factor 8.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 '(25 + x)' equal to zero and attempt to solve: Simplifying 25 + x = 0 Solving 25 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + x = 0 + -25 x = 0 + -25 Combine like terms: 0 + -25 = -25 x = -25 Simplifying x = -25Solution
x = {30, -25}
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