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Simplifying 2x2 + -250x = -5000 Reorder the terms: -250x + 2x2 = -5000 Solving -250x + 2x2 = -5000 Solving for variable 'x'. Reorder the terms: 5000 + -250x + 2x2 = -5000 + 5000 Combine like terms: -5000 + 5000 = 0 5000 + -250x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2500 + -125x + x2) = 0 Factor a trinomial. 2((25 + -1x)(100 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 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 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Divide each side by '-1'. x = 25 Simplifying x = 25Subproblem 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 = {25, 100}
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