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Simplifying (2x2) + -1x + -100000 = 0 Reorder the terms: -100000 + -1x + (2x2) = 0 Solving -100000 + -1x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50000 + -0.5x + x2 = 0 Move the constant term to the right: Add '50000' to each side of the equation. -50000 + -0.5x + 50000 + x2 = 0 + 50000 Reorder the terms: -50000 + 50000 + -0.5x + x2 = 0 + 50000 Combine like terms: -50000 + 50000 = 0 0 + -0.5x + x2 = 0 + 50000 -0.5x + x2 = 0 + 50000 Combine like terms: 0 + 50000 = 50000 -0.5x + x2 = 50000 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 50000 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 50000 + 0.0625 Combine like terms: 50000 + 0.0625 = 50000.0625 0.0625 + -0.5x + x2 = 50000.0625 Factor a perfect square on the left side: ((x) + -0.25)((x) + -0.25) = 50000.0625 Calculate the square root of the right side: 223.606937504 Break this problem into two subproblems by setting ((x) + -0.25) equal to 223.606937504 and -223.606937504.Subproblem 1
(x) + -0.25 = 223.606937504 Simplifying (x) + -0.25 = 223.606937504 x + -0.25 = 223.606937504 Reorder the terms: -0.25 + x = 223.606937504 Solving -0.25 + x = 223.606937504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 223.606937504 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 223.606937504 + 0.25 x = 223.606937504 + 0.25 Combine like terms: 223.606937504 + 0.25 = 223.856937504 x = 223.856937504 Simplifying x = 223.856937504Subproblem 2
(x) + -0.25 = -223.606937504 Simplifying (x) + -0.25 = -223.606937504 x + -0.25 = -223.606937504 Reorder the terms: -0.25 + x = -223.606937504 Solving -0.25 + x = -223.606937504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -223.606937504 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -223.606937504 + 0.25 x = -223.606937504 + 0.25 Combine like terms: -223.606937504 + 0.25 = -223.356937504 x = -223.356937504 Simplifying x = -223.356937504Solution
The solution to the problem is based on the solutions from the subproblems. x = {223.856937504, -223.356937504}
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