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Simplifying 2800 = 700 + 1000x + -100x2 Solving 2800 = 700 + 1000x + -100x2 Solving for variable 'x'. Combine like terms: 2800 + -700 = 2100 2100 + -1000x + 100x2 = 700 + 1000x + -100x2 + -700 + -1000x + 100x2 Reorder the terms: 2100 + -1000x + 100x2 = 700 + -700 + 1000x + -1000x + -100x2 + 100x2 Combine like terms: 700 + -700 = 0 2100 + -1000x + 100x2 = 0 + 1000x + -1000x + -100x2 + 100x2 2100 + -1000x + 100x2 = 1000x + -1000x + -100x2 + 100x2 Combine like terms: 1000x + -1000x = 0 2100 + -1000x + 100x2 = 0 + -100x2 + 100x2 2100 + -1000x + 100x2 = -100x2 + 100x2 Combine like terms: -100x2 + 100x2 = 0 2100 + -1000x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(21 + -10x + x2) = 0 Factor a trinomial. 100((3 + -1x)(7 + -1x)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {3, 7}
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