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Simplifying (1000 + -50x)(1000 + -50x) = 0 Multiply (1000 + -50x) * (1000 + -50x) (1000(1000 + -50x) + -50x * (1000 + -50x)) = 0 ((1000 * 1000 + -50x * 1000) + -50x * (1000 + -50x)) = 0 ((1000000 + -50000x) + -50x * (1000 + -50x)) = 0 (1000000 + -50000x + (1000 * -50x + -50x * -50x)) = 0 (1000000 + -50000x + (-50000x + 2500x2)) = 0 Combine like terms: -50000x + -50000x = -100000x (1000000 + -100000x + 2500x2) = 0 Solving 1000000 + -100000x + 2500x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2500'. 2500(400 + -40x + x2) = 0 Factor a trinomial. 2500((20 + -1x)(20 + -1x)) = 0 Ignore the factor 2500.Subproblem 1
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 = 20Subproblem 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 = {20, 20}
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