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Simplifying 21400 + 200 = 300x + -1x2 Combine like terms: 21400 + 200 = 21600 21600 = 300x + -1x2 Solving 21600 = 300x + -1x2 Solving for variable 'x'. Reorder the terms: 21600 + -300x + x2 = 300x + -300x + -1x2 + x2 Combine like terms: 300x + -300x = 0 21600 + -300x + x2 = 0 + -1x2 + x2 21600 + -300x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 21600 + -300x + x2 = 0 Factor a trinomial. (120 + -1x)(180 + -1x) = 0Subproblem 1
Set the factor '(120 + -1x)' equal to zero and attempt to solve: Simplifying 120 + -1x = 0 Solving 120 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + -1x = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -1x = 0 + -120 -1x = 0 + -120 Combine like terms: 0 + -120 = -120 -1x = -120 Divide each side by '-1'. x = 120 Simplifying x = 120Subproblem 2
Set the factor '(180 + -1x)' equal to zero and attempt to solve: Simplifying 180 + -1x = 0 Solving 180 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-180' to each side of the equation. 180 + -180 + -1x = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -1x = 0 + -180 -1x = 0 + -180 Combine like terms: 0 + -180 = -180 -1x = -180 Divide each side by '-1'. x = 180 Simplifying x = 180Solution
x = {120, 180}
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