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Simplifying 300x + -3x2 = 7500 Solving 300x + -3x2 = 7500 Solving for variable 'x'. Reorder the terms: -7500 + 300x + -3x2 = 7500 + -7500 Combine like terms: 7500 + -7500 = 0 -7500 + 300x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2500 + 100x + -1x2) = 0 Factor a trinomial. 3((-50 + x)(50 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-50 + x)' equal to zero and attempt to solve: Simplifying -50 + x = 0 Solving -50 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + x = 0 + 50 x = 0 + 50 Combine like terms: 0 + 50 = 50 x = 50 Simplifying x = 50Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50Solution
x = {50, 50}
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