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Simplifying x = 1520x + -1x2 + -108000 Reorder the terms: x = -108000 + 1520x + -1x2 Solving x = -108000 + 1520x + -1x2 Solving for variable 'x'. Reorder the terms: 108000 + x + -1520x + x2 = -108000 + 1520x + -1x2 + 108000 + -1520x + x2 Combine like terms: x + -1520x = -1519x 108000 + -1519x + x2 = -108000 + 1520x + -1x2 + 108000 + -1520x + x2 Reorder the terms: 108000 + -1519x + x2 = -108000 + 108000 + 1520x + -1520x + -1x2 + x2 Combine like terms: -108000 + 108000 = 0 108000 + -1519x + x2 = 0 + 1520x + -1520x + -1x2 + x2 108000 + -1519x + x2 = 1520x + -1520x + -1x2 + x2 Combine like terms: 1520x + -1520x = 0 108000 + -1519x + x2 = 0 + -1x2 + x2 108000 + -1519x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 108000 + -1519x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-108000' to each side of the equation. 108000 + -1519x + -108000 + x2 = 0 + -108000 Reorder the terms: 108000 + -108000 + -1519x + x2 = 0 + -108000 Combine like terms: 108000 + -108000 = 0 0 + -1519x + x2 = 0 + -108000 -1519x + x2 = 0 + -108000 Combine like terms: 0 + -108000 = -108000 -1519x + x2 = -108000 The x term is -1519x. Take half its coefficient (-759.5). Square it (576840.25) and add it to both sides. Add '576840.25' to each side of the equation. -1519x + 576840.25 + x2 = -108000 + 576840.25 Reorder the terms: 576840.25 + -1519x + x2 = -108000 + 576840.25 Combine like terms: -108000 + 576840.25 = 468840.25 576840.25 + -1519x + x2 = 468840.25 Factor a perfect square on the left side: (x + -759.5)(x + -759.5) = 468840.25 Calculate the square root of the right side: 684.71910299 Break this problem into two subproblems by setting (x + -759.5) equal to 684.71910299 and -684.71910299.Subproblem 1
x + -759.5 = 684.71910299 Simplifying x + -759.5 = 684.71910299 Reorder the terms: -759.5 + x = 684.71910299 Solving -759.5 + x = 684.71910299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '759.5' to each side of the equation. -759.5 + 759.5 + x = 684.71910299 + 759.5 Combine like terms: -759.5 + 759.5 = 0.0 0.0 + x = 684.71910299 + 759.5 x = 684.71910299 + 759.5 Combine like terms: 684.71910299 + 759.5 = 1444.21910299 x = 1444.21910299 Simplifying x = 1444.21910299Subproblem 2
x + -759.5 = -684.71910299 Simplifying x + -759.5 = -684.71910299 Reorder the terms: -759.5 + x = -684.71910299 Solving -759.5 + x = -684.71910299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '759.5' to each side of the equation. -759.5 + 759.5 + x = -684.71910299 + 759.5 Combine like terms: -759.5 + 759.5 = 0.0 0.0 + x = -684.71910299 + 759.5 x = -684.71910299 + 759.5 Combine like terms: -684.71910299 + 759.5 = 74.78089701 x = 74.78089701 Simplifying x = 74.78089701Solution
The solution to the problem is based on the solutions from the subproblems. x = {1444.21910299, 74.78089701}
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