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Simplifying 2x2 + -1x + -2000 = 0 Reorder the terms: -2000 + -1x + 2x2 = 0 Solving -2000 + -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'. -1000 + -0.5x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -0.5x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -0.5x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -0.5x + x2 = 0 + 1000 -0.5x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -0.5x + x2 = 1000 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 = 1000 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1000 + 0.0625 Combine like terms: 1000 + 0.0625 = 1000.0625 0.0625 + -0.5x + x2 = 1000.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1000.0625 Calculate the square root of the right side: 31.623764798 Break this problem into two subproblems by setting (x + -0.25) equal to 31.623764798 and -31.623764798.Subproblem 1
x + -0.25 = 31.623764798 Simplifying x + -0.25 = 31.623764798 Reorder the terms: -0.25 + x = 31.623764798 Solving -0.25 + x = 31.623764798 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 = 31.623764798 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 31.623764798 + 0.25 x = 31.623764798 + 0.25 Combine like terms: 31.623764798 + 0.25 = 31.873764798 x = 31.873764798 Simplifying x = 31.873764798Subproblem 2
x + -0.25 = -31.623764798 Simplifying x + -0.25 = -31.623764798 Reorder the terms: -0.25 + x = -31.623764798 Solving -0.25 + x = -31.623764798 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 = -31.623764798 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -31.623764798 + 0.25 x = -31.623764798 + 0.25 Combine like terms: -31.623764798 + 0.25 = -31.373764798 x = -31.373764798 Simplifying x = -31.373764798Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.873764798, -31.373764798}
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