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Simplifying 80000 = x2 + 2400x + -1320000 Reorder the terms: 80000 = -1320000 + 2400x + x2 Solving 80000 = -1320000 + 2400x + x2 Solving for variable 'x'. Combine like terms: 80000 + 1320000 = 1400000 1400000 + -2400x + -1x2 = -1320000 + 2400x + x2 + 1320000 + -2400x + -1x2 Reorder the terms: 1400000 + -2400x + -1x2 = -1320000 + 1320000 + 2400x + -2400x + x2 + -1x2 Combine like terms: -1320000 + 1320000 = 0 1400000 + -2400x + -1x2 = 0 + 2400x + -2400x + x2 + -1x2 1400000 + -2400x + -1x2 = 2400x + -2400x + x2 + -1x2 Combine like terms: 2400x + -2400x = 0 1400000 + -2400x + -1x2 = 0 + x2 + -1x2 1400000 + -2400x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1400000 + -2400x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1400000 + 2400x + x2 = 0 Move the constant term to the right: Add '1400000' to each side of the equation. -1400000 + 2400x + 1400000 + x2 = 0 + 1400000 Reorder the terms: -1400000 + 1400000 + 2400x + x2 = 0 + 1400000 Combine like terms: -1400000 + 1400000 = 0 0 + 2400x + x2 = 0 + 1400000 2400x + x2 = 0 + 1400000 Combine like terms: 0 + 1400000 = 1400000 2400x + x2 = 1400000 The x term is 2400x. Take half its coefficient (1200). Square it (1440000) and add it to both sides. Add '1440000' to each side of the equation. 2400x + 1440000 + x2 = 1400000 + 1440000 Reorder the terms: 1440000 + 2400x + x2 = 1400000 + 1440000 Combine like terms: 1400000 + 1440000 = 2840000 1440000 + 2400x + x2 = 2840000 Factor a perfect square on the left side: (x + 1200)(x + 1200) = 2840000 Calculate the square root of the right side: 1685.229954635 Break this problem into two subproblems by setting (x + 1200) equal to 1685.229954635 and -1685.229954635.Subproblem 1
x + 1200 = 1685.229954635 Simplifying x + 1200 = 1685.229954635 Reorder the terms: 1200 + x = 1685.229954635 Solving 1200 + x = 1685.229954635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1200' to each side of the equation. 1200 + -1200 + x = 1685.229954635 + -1200 Combine like terms: 1200 + -1200 = 0 0 + x = 1685.229954635 + -1200 x = 1685.229954635 + -1200 Combine like terms: 1685.229954635 + -1200 = 485.229954635 x = 485.229954635 Simplifying x = 485.229954635Subproblem 2
x + 1200 = -1685.229954635 Simplifying x + 1200 = -1685.229954635 Reorder the terms: 1200 + x = -1685.229954635 Solving 1200 + x = -1685.229954635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1200' to each side of the equation. 1200 + -1200 + x = -1685.229954635 + -1200 Combine like terms: 1200 + -1200 = 0 0 + x = -1685.229954635 + -1200 x = -1685.229954635 + -1200 Combine like terms: -1685.229954635 + -1200 = -2885.229954635 x = -2885.229954635 Simplifying x = -2885.229954635Solution
The solution to the problem is based on the solutions from the subproblems. x = {485.229954635, -2885.229954635}
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