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Simplifying x2 + -2000x + -200000 = 0 Reorder the terms: -200000 + -2000x + x2 = 0 Solving -200000 + -2000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200000' to each side of the equation. -200000 + -2000x + 200000 + x2 = 0 + 200000 Reorder the terms: -200000 + 200000 + -2000x + x2 = 0 + 200000 Combine like terms: -200000 + 200000 = 0 0 + -2000x + x2 = 0 + 200000 -2000x + x2 = 0 + 200000 Combine like terms: 0 + 200000 = 200000 -2000x + x2 = 200000 The x term is -2000x. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000x + 1000000 + x2 = 200000 + 1000000 Reorder the terms: 1000000 + -2000x + x2 = 200000 + 1000000 Combine like terms: 200000 + 1000000 = 1200000 1000000 + -2000x + x2 = 1200000 Factor a perfect square on the left side: (x + -1000)(x + -1000) = 1200000 Calculate the square root of the right side: 1095.44511501 Break this problem into two subproblems by setting (x + -1000) equal to 1095.44511501 and -1095.44511501.Subproblem 1
x + -1000 = 1095.44511501 Simplifying x + -1000 = 1095.44511501 Reorder the terms: -1000 + x = 1095.44511501 Solving -1000 + x = 1095.44511501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = 1095.44511501 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = 1095.44511501 + 1000 x = 1095.44511501 + 1000 Combine like terms: 1095.44511501 + 1000 = 2095.44511501 x = 2095.44511501 Simplifying x = 2095.44511501Subproblem 2
x + -1000 = -1095.44511501 Simplifying x + -1000 = -1095.44511501 Reorder the terms: -1000 + x = -1095.44511501 Solving -1000 + x = -1095.44511501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = -1095.44511501 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = -1095.44511501 + 1000 x = -1095.44511501 + 1000 Combine like terms: -1095.44511501 + 1000 = -95.44511501 x = -95.44511501 Simplifying x = -95.44511501Solution
The solution to the problem is based on the solutions from the subproblems. x = {2095.44511501, -95.44511501}
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