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Simplifying 17600 = -50x2 + 1500x + 14800 Reorder the terms: 17600 = 14800 + 1500x + -50x2 Solving 17600 = 14800 + 1500x + -50x2 Solving for variable 'x'. Combine like terms: 17600 + -14800 = 2800 2800 + -1500x + 50x2 = 14800 + 1500x + -50x2 + -14800 + -1500x + 50x2 Reorder the terms: 2800 + -1500x + 50x2 = 14800 + -14800 + 1500x + -1500x + -50x2 + 50x2 Combine like terms: 14800 + -14800 = 0 2800 + -1500x + 50x2 = 0 + 1500x + -1500x + -50x2 + 50x2 2800 + -1500x + 50x2 = 1500x + -1500x + -50x2 + 50x2 Combine like terms: 1500x + -1500x = 0 2800 + -1500x + 50x2 = 0 + -50x2 + 50x2 2800 + -1500x + 50x2 = -50x2 + 50x2 Combine like terms: -50x2 + 50x2 = 0 2800 + -1500x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(56 + -30x + x2) = 0 Factor a trinomial. 50((2 + -1x)(28 + -1x)) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(28 + -1x)' equal to zero and attempt to solve: Simplifying 28 + -1x = 0 Solving 28 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + -1x = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -1x = 0 + -28 -1x = 0 + -28 Combine like terms: 0 + -28 = -28 -1x = -28 Divide each side by '-1'. x = 28 Simplifying x = 28Solution
x = {2, 28}
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