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Simplifying x(x + -1) = 50000 Reorder the terms: x(-1 + x) = 50000 (-1 * x + x * x) = 50000 (-1x + x2) = 50000 Solving -1x + x2 = 50000 Solving for variable 'x'. Reorder the terms: -50000 + -1x + x2 = 50000 + -50000 Combine like terms: 50000 + -50000 = 0 -50000 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50000' to each side of the equation. -50000 + -1x + 50000 + x2 = 0 + 50000 Reorder the terms: -50000 + 50000 + -1x + x2 = 0 + 50000 Combine like terms: -50000 + 50000 = 0 0 + -1x + x2 = 0 + 50000 -1x + x2 = 0 + 50000 Combine like terms: 0 + 50000 = 50000 -1x + x2 = 50000 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 = 50000 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 50000 + 0.25 Combine like terms: 50000 + 0.25 = 50000.25 0.25 + -1x + x2 = 50000.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 50000.25 Calculate the square root of the right side: 223.607356766 Break this problem into two subproblems by setting (x + -0.5) equal to 223.607356766 and -223.607356766.Subproblem 1
x + -0.5 = 223.607356766 Simplifying x + -0.5 = 223.607356766 Reorder the terms: -0.5 + x = 223.607356766 Solving -0.5 + x = 223.607356766 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 = 223.607356766 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 223.607356766 + 0.5 x = 223.607356766 + 0.5 Combine like terms: 223.607356766 + 0.5 = 224.107356766 x = 224.107356766 Simplifying x = 224.107356766Subproblem 2
x + -0.5 = -223.607356766 Simplifying x + -0.5 = -223.607356766 Reorder the terms: -0.5 + x = -223.607356766 Solving -0.5 + x = -223.607356766 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 = -223.607356766 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -223.607356766 + 0.5 x = -223.607356766 + 0.5 Combine like terms: -223.607356766 + 0.5 = -223.107356766 x = -223.107356766 Simplifying x = -223.107356766Solution
The solution to the problem is based on the solutions from the subproblems. x = {224.107356766, -223.107356766}
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