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Simplifying 5600 = 200 + 1500x + -100x2 Solving 5600 = 200 + 1500x + -100x2 Solving for variable 'x'. Combine like terms: 5600 + -200 = 5400 5400 + -1500x + 100x2 = 200 + 1500x + -100x2 + -200 + -1500x + 100x2 Reorder the terms: 5400 + -1500x + 100x2 = 200 + -200 + 1500x + -1500x + -100x2 + 100x2 Combine like terms: 200 + -200 = 0 5400 + -1500x + 100x2 = 0 + 1500x + -1500x + -100x2 + 100x2 5400 + -1500x + 100x2 = 1500x + -1500x + -100x2 + 100x2 Combine like terms: 1500x + -1500x = 0 5400 + -1500x + 100x2 = 0 + -100x2 + 100x2 5400 + -1500x + 100x2 = -100x2 + 100x2 Combine like terms: -100x2 + 100x2 = 0 5400 + -1500x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(54 + -15x + x2) = 0 Factor a trinomial. 100((6 + -1x)(9 + -1x)) = 0 Ignore the factor 100.Subproblem 1
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 = 6Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {6, 9}
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