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Simplifying (50 + -2x) * x = 200 Reorder the terms for easier multiplication: x(50 + -2x) = 200 (50 * x + -2x * x) = 200 (50x + -2x2) = 200 Solving 50x + -2x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 50x + -2x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 50x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + 25x + -1x2) = 0 Factor a trinomial. 2((-20 + x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve: Simplifying -20 + x = 0 Solving -20 + x = 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 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Simplifying x = 20Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {20, 5}
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