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Simplifying 54600 = 750x + -75x2 + 52800 Reorder the terms: 54600 = 52800 + 750x + -75x2 Solving 54600 = 52800 + 750x + -75x2 Solving for variable 'x'. Combine like terms: 54600 + -52800 = 1800 1800 + -750x + 75x2 = 52800 + 750x + -75x2 + -52800 + -750x + 75x2 Reorder the terms: 1800 + -750x + 75x2 = 52800 + -52800 + 750x + -750x + -75x2 + 75x2 Combine like terms: 52800 + -52800 = 0 1800 + -750x + 75x2 = 0 + 750x + -750x + -75x2 + 75x2 1800 + -750x + 75x2 = 750x + -750x + -75x2 + 75x2 Combine like terms: 750x + -750x = 0 1800 + -750x + 75x2 = 0 + -75x2 + 75x2 1800 + -750x + 75x2 = -75x2 + 75x2 Combine like terms: -75x2 + 75x2 = 0 1800 + -750x + 75x2 = 0 Factor out the Greatest Common Factor (GCF), '75'. 75(24 + -10x + x2) = 0 Factor a trinomial. 75((4 + -1x)(6 + -1x)) = 0 Ignore the factor 75.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {4, 6}
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