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Simplifying 1000x2 + 100001x + 1000 = 0 Reorder the terms: 1000 + 100001x + 1000x2 = 0 Solving 1000 + 100001x + 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'. 1 + 100.001x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 100.001x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 100.001x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 100.001x + x2 = 0 + -1 100.001x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 100.001x + x2 = -1 The x term is 100.001x. Take half its coefficient (50.0005). Square it (2500.050000) and add it to both sides. Add '2500.050000' to each side of the equation. 100.001x + 2500.050000 + x2 = -1 + 2500.050000 Reorder the terms: 2500.050000 + 100.001x + x2 = -1 + 2500.050000 Combine like terms: -1 + 2500.050000 = 2499.05 2500.050000 + 100.001x + x2 = 2499.05 Factor a perfect square on the left side: (x + 50.0005)(x + 50.0005) = 2499.05 Calculate the square root of the right side: 49.990499097 Break this problem into two subproblems by setting (x + 50.0005) equal to 49.990499097 and -49.990499097.Subproblem 1
x + 50.0005 = 49.990499097 Simplifying x + 50.0005 = 49.990499097 Reorder the terms: 50.0005 + x = 49.990499097 Solving 50.0005 + x = 49.990499097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.0005' to each side of the equation. 50.0005 + -50.0005 + x = 49.990499097 + -50.0005 Combine like terms: 50.0005 + -50.0005 = 0.0000 0.0000 + x = 49.990499097 + -50.0005 x = 49.990499097 + -50.0005 Combine like terms: 49.990499097 + -50.0005 = -0.010000903 x = -0.010000903 Simplifying x = -0.010000903Subproblem 2
x + 50.0005 = -49.990499097 Simplifying x + 50.0005 = -49.990499097 Reorder the terms: 50.0005 + x = -49.990499097 Solving 50.0005 + x = -49.990499097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.0005' to each side of the equation. 50.0005 + -50.0005 + x = -49.990499097 + -50.0005 Combine like terms: 50.0005 + -50.0005 = 0.0000 0.0000 + x = -49.990499097 + -50.0005 x = -49.990499097 + -50.0005 Combine like terms: -49.990499097 + -50.0005 = -99.990999097 x = -99.990999097 Simplifying x = -99.990999097Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.010000903, -99.990999097}
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