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Simplifying 1000000 + -2000.083x + x2 = 0 Solving 1000000 + -2000.083x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1000000' to each side of the equation. 1000000 + -2000.083x + -1000000 + x2 = 0 + -1000000 Reorder the terms: 1000000 + -1000000 + -2000.083x + x2 = 0 + -1000000 Combine like terms: 1000000 + -1000000 = 0 0 + -2000.083x + x2 = 0 + -1000000 -2000.083x + x2 = 0 + -1000000 Combine like terms: 0 + -1000000 = -1000000 -2000.083x + x2 = -1000000 The x term is -2000.083x. Take half its coefficient (-1000.0415). Square it (1000083.002) and add it to both sides. Add '1000083.002' to each side of the equation. -2000.083x + 1000083.002 + x2 = -1000000 + 1000083.002 Reorder the terms: 1000083.002 + -2000.083x + x2 = -1000000 + 1000083.002 Combine like terms: -1000000 + 1000083.002 = 83.002 1000083.002 + -2000.083x + x2 = 83.002 Factor a perfect square on the left side: (x + -1000.0415)(x + -1000.0415) = 83.002 Calculate the square root of the right side: 9.110543343 Break this problem into two subproblems by setting (x + -1000.0415) equal to 9.110543343 and -9.110543343.Subproblem 1
x + -1000.0415 = 9.110543343 Simplifying x + -1000.0415 = 9.110543343 Reorder the terms: -1000.0415 + x = 9.110543343 Solving -1000.0415 + x = 9.110543343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000.0415' to each side of the equation. -1000.0415 + 1000.0415 + x = 9.110543343 + 1000.0415 Combine like terms: -1000.0415 + 1000.0415 = 0.0000 0.0000 + x = 9.110543343 + 1000.0415 x = 9.110543343 + 1000.0415 Combine like terms: 9.110543343 + 1000.0415 = 1009.152043343 x = 1009.152043343 Simplifying x = 1009.152043343Subproblem 2
x + -1000.0415 = -9.110543343 Simplifying x + -1000.0415 = -9.110543343 Reorder the terms: -1000.0415 + x = -9.110543343 Solving -1000.0415 + x = -9.110543343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000.0415' to each side of the equation. -1000.0415 + 1000.0415 + x = -9.110543343 + 1000.0415 Combine like terms: -1000.0415 + 1000.0415 = 0.0000 0.0000 + x = -9.110543343 + 1000.0415 x = -9.110543343 + 1000.0415 Combine like terms: -9.110543343 + 1000.0415 = 990.930956657 x = 990.930956657 Simplifying x = 990.930956657Solution
The solution to the problem is based on the solutions from the subproblems. x = {1009.152043343, 990.930956657}
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