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Simplifying x(x + -1) = 100000 Reorder the terms: x(-1 + x) = 100000 (-1 * x + x * x) = 100000 (-1x + x2) = 100000 Solving -1x + x2 = 100000 Solving for variable 'x'. Reorder the terms: -100000 + -1x + x2 = 100000 + -100000 Combine like terms: 100000 + -100000 = 0 -100000 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100000' to each side of the equation. -100000 + -1x + 100000 + x2 = 0 + 100000 Reorder the terms: -100000 + 100000 + -1x + x2 = 0 + 100000 Combine like terms: -100000 + 100000 = 0 0 + -1x + x2 = 0 + 100000 -1x + x2 = 0 + 100000 Combine like terms: 0 + 100000 = 100000 -1x + x2 = 100000 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 = 100000 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 100000 + 0.25 Combine like terms: 100000 + 0.25 = 100000.25 0.25 + -1x + x2 = 100000.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 100000.25 Calculate the square root of the right side: 316.228161301 Break this problem into two subproblems by setting (x + -0.5) equal to 316.228161301 and -316.228161301.Subproblem 1
x + -0.5 = 316.228161301 Simplifying x + -0.5 = 316.228161301 Reorder the terms: -0.5 + x = 316.228161301 Solving -0.5 + x = 316.228161301 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 = 316.228161301 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 316.228161301 + 0.5 x = 316.228161301 + 0.5 Combine like terms: 316.228161301 + 0.5 = 316.728161301 x = 316.728161301 Simplifying x = 316.728161301Subproblem 2
x + -0.5 = -316.228161301 Simplifying x + -0.5 = -316.228161301 Reorder the terms: -0.5 + x = -316.228161301 Solving -0.5 + x = -316.228161301 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 = -316.228161301 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -316.228161301 + 0.5 x = -316.228161301 + 0.5 Combine like terms: -316.228161301 + 0.5 = -315.728161301 x = -315.728161301 Simplifying x = -315.728161301Solution
The solution to the problem is based on the solutions from the subproblems. x = {316.728161301, -315.728161301}
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