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Simplifying 1300 = -1x2 + 2400x + -1320000 Reorder the terms: 1300 = -1320000 + 2400x + -1x2 Solving 1300 = -1320000 + 2400x + -1x2 Solving for variable 'x'. Combine like terms: 1300 + 1320000 = 1321300 1321300 + -2400x + x2 = -1320000 + 2400x + -1x2 + 1320000 + -2400x + x2 Reorder the terms: 1321300 + -2400x + x2 = -1320000 + 1320000 + 2400x + -2400x + -1x2 + x2 Combine like terms: -1320000 + 1320000 = 0 1321300 + -2400x + x2 = 0 + 2400x + -2400x + -1x2 + x2 1321300 + -2400x + x2 = 2400x + -2400x + -1x2 + x2 Combine like terms: 2400x + -2400x = 0 1321300 + -2400x + x2 = 0 + -1x2 + x2 1321300 + -2400x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1321300 + -2400x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1321300' to each side of the equation. 1321300 + -2400x + -1321300 + x2 = 0 + -1321300 Reorder the terms: 1321300 + -1321300 + -2400x + x2 = 0 + -1321300 Combine like terms: 1321300 + -1321300 = 0 0 + -2400x + x2 = 0 + -1321300 -2400x + x2 = 0 + -1321300 Combine like terms: 0 + -1321300 = -1321300 -2400x + x2 = -1321300 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 = -1321300 + 1440000 Reorder the terms: 1440000 + -2400x + x2 = -1321300 + 1440000 Combine like terms: -1321300 + 1440000 = 118700 1440000 + -2400x + x2 = 118700 Factor a perfect square on the left side: (x + -1200)(x + -1200) = 118700 Calculate the square root of the right side: 344.528663539 Break this problem into two subproblems by setting (x + -1200) equal to 344.528663539 and -344.528663539.Subproblem 1
x + -1200 = 344.528663539 Simplifying x + -1200 = 344.528663539 Reorder the terms: -1200 + x = 344.528663539 Solving -1200 + x = 344.528663539 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 = 344.528663539 + 1200 Combine like terms: -1200 + 1200 = 0 0 + x = 344.528663539 + 1200 x = 344.528663539 + 1200 Combine like terms: 344.528663539 + 1200 = 1544.528663539 x = 1544.528663539 Simplifying x = 1544.528663539Subproblem 2
x + -1200 = -344.528663539 Simplifying x + -1200 = -344.528663539 Reorder the terms: -1200 + x = -344.528663539 Solving -1200 + x = -344.528663539 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 = -344.528663539 + 1200 Combine like terms: -1200 + 1200 = 0 0 + x = -344.528663539 + 1200 x = -344.528663539 + 1200 Combine like terms: -344.528663539 + 1200 = 855.471336461 x = 855.471336461 Simplifying x = 855.471336461Solution
The solution to the problem is based on the solutions from the subproblems. x = {1544.528663539, 855.471336461}
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