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Simplifying 0 = -1x2 + 100x + -2400 Reorder the terms: 0 = -2400 + 100x + -1x2 Solving 0 = -2400 + 100x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 2400 = 2400 2400 + -100x + x2 = -2400 + 100x + -1x2 + 2400 + -100x + x2 Reorder the terms: 2400 + -100x + x2 = -2400 + 2400 + 100x + -100x + -1x2 + x2 Combine like terms: -2400 + 2400 = 0 2400 + -100x + x2 = 0 + 100x + -100x + -1x2 + x2 2400 + -100x + x2 = 100x + -100x + -1x2 + x2 Combine like terms: 100x + -100x = 0 2400 + -100x + x2 = 0 + -1x2 + x2 2400 + -100x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 2400 + -100x + x2 = 0 Factor a trinomial. (40 + -1x)(60 + -1x) = 0Subproblem 1
Set the factor '(40 + -1x)' equal to zero and attempt to solve: Simplifying 40 + -1x = 0 Solving 40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1x = 0 + -40 -1x = 0 + -40 Combine like terms: 0 + -40 = -40 -1x = -40 Divide each side by '-1'. x = 40 Simplifying x = 40Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Solution
x = {40, 60}
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