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Simplifying 0 = -10X2 + 100X + 12000 Reorder the terms: 0 = 12000 + 100X + -10X2 Solving 0 = 12000 + 100X + -10X2 Solving for variable 'X'. Combine like terms: 0 + -12000 = -12000 -12000 + -100X + 10X2 = 12000 + 100X + -10X2 + -12000 + -100X + 10X2 Reorder the terms: -12000 + -100X + 10X2 = 12000 + -12000 + 100X + -100X + -10X2 + 10X2 Combine like terms: 12000 + -12000 = 0 -12000 + -100X + 10X2 = 0 + 100X + -100X + -10X2 + 10X2 -12000 + -100X + 10X2 = 100X + -100X + -10X2 + 10X2 Combine like terms: 100X + -100X = 0 -12000 + -100X + 10X2 = 0 + -10X2 + 10X2 -12000 + -100X + 10X2 = -10X2 + 10X2 Combine like terms: -10X2 + 10X2 = 0 -12000 + -100X + 10X2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-1200 + -10X + X2) = 0 Factor a trinomial. 10((-30 + -1X)(40 + -1X)) = 0 Ignore the factor 10.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 '(40 + -1X)' equal to zero and attempt to solve: Simplifying 40 + -1X = 0 Solving 40 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1X = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1X = 0 + -40 -1X = 0 + -40 Combine like terms: 0 + -40 = -40 -1X = -40 Divide each side by '-1'. X = 40 Simplifying X = 40Solution
X = {-30, 40}
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