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Simplifying 450 = -25x2 + 75x + 450 Reorder the terms: 450 = 450 + 75x + -25x2 Add '-450' to each side of the equation. 450 + -450 = 450 + 75x + -450 + -25x2 Combine like terms: 450 + -450 = 0 0 = 450 + 75x + -450 + -25x2 Reorder the terms: 0 = 450 + -450 + 75x + -25x2 Combine like terms: 450 + -450 = 0 0 = 0 + 75x + -25x2 0 = 75x + -25x2 Solving 0 = 75x + -25x2 Solving for variable 'x'. Remove the zero: -75x + 25x2 = 75x + -25x2 + -75x + 25x2 Reorder the terms: -75x + 25x2 = 75x + -75x + -25x2 + 25x2 Combine like terms: 75x + -75x = 0 -75x + 25x2 = 0 + -25x2 + 25x2 -75x + 25x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 -75x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25x'. 25x(-3 + x) = 0 Ignore the factor 25.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Solution
x = {0, 3}
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