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Simplifying -5x2 + 1000x + 5000 = 55000 Reorder the terms: 5000 + 1000x + -5x2 = 55000 Solving 5000 + 1000x + -5x2 = 55000 Solving for variable 'x'. Reorder the terms: 5000 + -55000 + 1000x + -5x2 = 55000 + -55000 Combine like terms: 5000 + -55000 = -50000 -50000 + 1000x + -5x2 = 55000 + -55000 Combine like terms: 55000 + -55000 = 0 -50000 + 1000x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-10000 + 200x + -1x2) = 0 Factor a trinomial. 5((-100 + x)(100 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-100 + x)' equal to zero and attempt to solve: Simplifying -100 + x = 0 Solving -100 + x = 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 + x = 0 + 100 Combine like terms: -100 + 100 = 0 0 + x = 0 + 100 x = 0 + 100 Combine like terms: 0 + 100 = 100 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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