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Simplifying x(100 + -2x) = 1200 (100 * x + -2x * x) = 1200 (100x + -2x2) = 1200 Solving 100x + -2x2 = 1200 Solving for variable 'x'. Reorder the terms: -1200 + 100x + -2x2 = 1200 + -1200 Combine like terms: 1200 + -1200 = 0 -1200 + 100x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-600 + 50x + -1x2) = 0 Factor a trinomial. 2((-30 + x)(20 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Simplifying x = 30Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {30, 20}
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