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Simplifying 300x + -5x2 = 4000 Solving 300x + -5x2 = 4000 Solving for variable 'x'. Reorder the terms: -4000 + 300x + -5x2 = 4000 + -4000 Combine like terms: 4000 + -4000 = 0 -4000 + 300x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-800 + 60x + -1x2) = 0 Factor a trinomial. 5((-40 + x)(20 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-40 + x)' equal to zero and attempt to solve: Simplifying -40 + x = 0 Solving -40 + x = 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 + x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + x = 0 + 40 x = 0 + 40 Combine like terms: 0 + 40 = 40 x = 40 Simplifying x = 40Subproblem 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 = {40, 20}
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