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Simplifying 2000 = 5x2 + -200x + 4000 Reorder the terms: 2000 = 4000 + -200x + 5x2 Solving 2000 = 4000 + -200x + 5x2 Solving for variable 'x'. Combine like terms: 2000 + -4000 = -2000 -2000 + 200x + -5x2 = 4000 + -200x + 5x2 + -4000 + 200x + -5x2 Reorder the terms: -2000 + 200x + -5x2 = 4000 + -4000 + -200x + 200x + 5x2 + -5x2 Combine like terms: 4000 + -4000 = 0 -2000 + 200x + -5x2 = 0 + -200x + 200x + 5x2 + -5x2 -2000 + 200x + -5x2 = -200x + 200x + 5x2 + -5x2 Combine like terms: -200x + 200x = 0 -2000 + 200x + -5x2 = 0 + 5x2 + -5x2 -2000 + 200x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -2000 + 200x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-400 + 40x + -1x2) = 0 Factor a trinomial. 5((-20 + x)(20 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve: Simplifying -20 + x = 0 Solving -20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Simplifying x = 20Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {20, 20}
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