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Simplifying 1000x2 + -1000x + -806.25 = 0 Reorder the terms: -806.25 + -1000x + 1000x2 = 0 Solving -806.25 + -1000x + 1000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. -0.80625 + -1x + x2 = 0 Move the constant term to the right: Add '0.80625' to each side of the equation. -0.80625 + -1x + 0.80625 + x2 = 0 + 0.80625 Reorder the terms: -0.80625 + 0.80625 + -1x + x2 = 0 + 0.80625 Combine like terms: -0.80625 + 0.80625 = 0.00000 0.00000 + -1x + x2 = 0 + 0.80625 -1x + x2 = 0 + 0.80625 Combine like terms: 0 + 0.80625 = 0.80625 -1x + x2 = 0.80625 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 = 0.80625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.80625 + 0.25 Combine like terms: 0.80625 + 0.25 = 1.05625 0.25 + -1x + x2 = 1.05625 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.05625 Calculate the square root of the right side: 1.02774024 Break this problem into two subproblems by setting (x + -0.5) equal to 1.02774024 and -1.02774024.Subproblem 1
x + -0.5 = 1.02774024 Simplifying x + -0.5 = 1.02774024 Reorder the terms: -0.5 + x = 1.02774024 Solving -0.5 + x = 1.02774024 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 = 1.02774024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.02774024 + 0.5 x = 1.02774024 + 0.5 Combine like terms: 1.02774024 + 0.5 = 1.52774024 x = 1.52774024 Simplifying x = 1.52774024Subproblem 2
x + -0.5 = -1.02774024 Simplifying x + -0.5 = -1.02774024 Reorder the terms: -0.5 + x = -1.02774024 Solving -0.5 + x = -1.02774024 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 = -1.02774024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.02774024 + 0.5 x = -1.02774024 + 0.5 Combine like terms: -1.02774024 + 0.5 = -0.52774024 x = -0.52774024 Simplifying x = -0.52774024Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.52774024, -0.52774024}
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