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Simplifying -0.0519u2 + -0.1016u + 1.283 = 0 Reorder the terms: 1.283 + -0.1016u + -0.0519u2 = 0 Solving 1.283 + -0.1016u + -0.0519u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -0.0519 the coefficient of the squared term: Divide each side by '-0.0519'. -24.72061657 + 1.95761079u + u2 = 0 Move the constant term to the right: Add '24.72061657' to each side of the equation. -24.72061657 + 1.95761079u + 24.72061657 + u2 = 0 + 24.72061657 Reorder the terms: -24.72061657 + 24.72061657 + 1.95761079u + u2 = 0 + 24.72061657 Combine like terms: -24.72061657 + 24.72061657 = 0.00000000 0.00000000 + 1.95761079u + u2 = 0 + 24.72061657 1.95761079u + u2 = 0 + 24.72061657 Combine like terms: 0 + 24.72061657 = 24.72061657 1.95761079u + u2 = 24.72061657 The u term is 1.95761079u. Take half its coefficient (0.978805395). Square it (0.9580600013) and add it to both sides. Add '0.9580600013' to each side of the equation. 1.95761079u + 0.9580600013 + u2 = 24.72061657 + 0.9580600013 Reorder the terms: 0.9580600013 + 1.95761079u + u2 = 24.72061657 + 0.9580600013 Combine like terms: 24.72061657 + 0.9580600013 = 25.6786765713 0.9580600013 + 1.95761079u + u2 = 25.6786765713 Factor a perfect square on the left side: (u + 0.978805395)(u + 0.978805395) = 25.6786765713 Calculate the square root of the right side: 5.067413203 Break this problem into two subproblems by setting (u + 0.978805395) equal to 5.067413203 and -5.067413203.Subproblem 1
u + 0.978805395 = 5.067413203 Simplifying u + 0.978805395 = 5.067413203 Reorder the terms: 0.978805395 + u = 5.067413203 Solving 0.978805395 + u = 5.067413203 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.978805395' to each side of the equation. 0.978805395 + -0.978805395 + u = 5.067413203 + -0.978805395 Combine like terms: 0.978805395 + -0.978805395 = 0.000000000 0.000000000 + u = 5.067413203 + -0.978805395 u = 5.067413203 + -0.978805395 Combine like terms: 5.067413203 + -0.978805395 = 4.088607808 u = 4.088607808 Simplifying u = 4.088607808Subproblem 2
u + 0.978805395 = -5.067413203 Simplifying u + 0.978805395 = -5.067413203 Reorder the terms: 0.978805395 + u = -5.067413203 Solving 0.978805395 + u = -5.067413203 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.978805395' to each side of the equation. 0.978805395 + -0.978805395 + u = -5.067413203 + -0.978805395 Combine like terms: 0.978805395 + -0.978805395 = 0.000000000 0.000000000 + u = -5.067413203 + -0.978805395 u = -5.067413203 + -0.978805395 Combine like terms: -5.067413203 + -0.978805395 = -6.046218598 u = -6.046218598 Simplifying u = -6.046218598Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.088607808, -6.046218598}
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