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Simplifying 3900 = -1x2 + 300x + -16100 Reorder the terms: 3900 = -16100 + 300x + -1x2 Solving 3900 = -16100 + 300x + -1x2 Solving for variable 'x'. Combine like terms: 3900 + 16100 = 20000 20000 + -300x + x2 = -16100 + 300x + -1x2 + 16100 + -300x + x2 Reorder the terms: 20000 + -300x + x2 = -16100 + 16100 + 300x + -300x + -1x2 + x2 Combine like terms: -16100 + 16100 = 0 20000 + -300x + x2 = 0 + 300x + -300x + -1x2 + x2 20000 + -300x + x2 = 300x + -300x + -1x2 + x2 Combine like terms: 300x + -300x = 0 20000 + -300x + x2 = 0 + -1x2 + x2 20000 + -300x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 20000 + -300x + x2 = 0 Factor a trinomial. (100 + -1x)(200 + -1x) = 0Subproblem 1
Set the factor '(100 + -1x)' equal to zero and attempt to solve: Simplifying 100 + -1x = 0 Solving 100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1x = 0 + -100 -1x = 0 + -100 Combine like terms: 0 + -100 = -100 -1x = -100 Divide each side by '-1'. x = 100 Simplifying x = 100Subproblem 2
Set the factor '(200 + -1x)' equal to zero and attempt to solve: Simplifying 200 + -1x = 0 Solving 200 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + -1x = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -1x = 0 + -200 -1x = 0 + -200 Combine like terms: 0 + -200 = -200 -1x = -200 Divide each side by '-1'. x = 200 Simplifying x = 200Solution
x = {100, 200}
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