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Simplifying x2 + -1x = 2000 Reorder the terms: -1x + x2 = 2000 Solving -1x + x2 = 2000 Solving for variable 'x'. Reorder the terms: -2000 + -1x + x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -2000 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + -1x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -1x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -1x + x2 = 0 + 2000 -1x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -1x + x2 = 2000 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2000 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2000 + 0.25 Combine like terms: 2000 + 0.25 = 2000.25 0.25 + -1x + x2 = 2000.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2000.25 Calculate the square root of the right side: 44.724154548 Break this problem into two subproblems by setting (x + -0.5) equal to 44.724154548 and -44.724154548.Subproblem 1
x + -0.5 = 44.724154548 Simplifying x + -0.5 = 44.724154548 Reorder the terms: -0.5 + x = 44.724154548 Solving -0.5 + x = 44.724154548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 44.724154548 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 44.724154548 + 0.5 x = 44.724154548 + 0.5 Combine like terms: 44.724154548 + 0.5 = 45.224154548 x = 45.224154548 Simplifying x = 45.224154548Subproblem 2
x + -0.5 = -44.724154548 Simplifying x + -0.5 = -44.724154548 Reorder the terms: -0.5 + x = -44.724154548 Solving -0.5 + x = -44.724154548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -44.724154548 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -44.724154548 + 0.5 x = -44.724154548 + 0.5 Combine like terms: -44.724154548 + 0.5 = -44.224154548 x = -44.224154548 Simplifying x = -44.224154548Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.224154548, -44.224154548}
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