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Simplifying 55000 = -5X2 + 1000X + 5000 Reorder the terms: 55000 = 5000 + 1000X + -5X2 Solving 55000 = 5000 + 1000X + -5X2 Solving for variable 'X'. Combine like terms: 55000 + -5000 = 50000 50000 + -1000X + 5X2 = 5000 + 1000X + -5X2 + -5000 + -1000X + 5X2 Reorder the terms: 50000 + -1000X + 5X2 = 5000 + -5000 + 1000X + -1000X + -5X2 + 5X2 Combine like terms: 5000 + -5000 = 0 50000 + -1000X + 5X2 = 0 + 1000X + -1000X + -5X2 + 5X2 50000 + -1000X + 5X2 = 1000X + -1000X + -5X2 + 5X2 Combine like terms: 1000X + -1000X = 0 50000 + -1000X + 5X2 = 0 + -5X2 + 5X2 50000 + -1000X + 5X2 = -5X2 + 5X2 Combine like terms: -5X2 + 5X2 = 0 50000 + -1000X + 5X2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(10000 + -200X + X2) = 0 Factor a trinomial. 5((100 + -1X)(100 + -1X)) = 0 Ignore the factor 5.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 '(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 = 100Solution
X = {100, 100}
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