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Simplifying 80000 = -1x2 + 2400x + -1320000 Reorder the terms: 80000 = -1320000 + 2400x + -1x2 Solving 80000 = -1320000 + 2400x + -1x2 Solving for variable 'x'. Combine like terms: 80000 + 1320000 = 1400000 1400000 + -2400x + x2 = -1320000 + 2400x + -1x2 + 1320000 + -2400x + x2 Reorder the terms: 1400000 + -2400x + x2 = -1320000 + 1320000 + 2400x + -2400x + -1x2 + x2 Combine like terms: -1320000 + 1320000 = 0 1400000 + -2400x + x2 = 0 + 2400x + -2400x + -1x2 + x2 1400000 + -2400x + x2 = 2400x + -2400x + -1x2 + x2 Combine like terms: 2400x + -2400x = 0 1400000 + -2400x + x2 = 0 + -1x2 + x2 1400000 + -2400x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1400000 + -2400x + x2 = 0 Factor a trinomial. (1000 + -1x)(1400 + -1x) = 0Subproblem 1
Set the factor '(1000 + -1x)' equal to zero and attempt to solve: Simplifying 1000 + -1x = 0 Solving 1000 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1000' to each side of the equation. 1000 + -1000 + -1x = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -1x = 0 + -1000 -1x = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -1x = -1000 Divide each side by '-1'. x = 1000 Simplifying x = 1000Subproblem 2
Set the factor '(1400 + -1x)' equal to zero and attempt to solve: Simplifying 1400 + -1x = 0 Solving 1400 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1400' to each side of the equation. 1400 + -1400 + -1x = 0 + -1400 Combine like terms: 1400 + -1400 = 0 0 + -1x = 0 + -1400 -1x = 0 + -1400 Combine like terms: 0 + -1400 = -1400 -1x = -1400 Divide each side by '-1'. x = 1400 Simplifying x = 1400Solution
x = {1000, 1400}
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