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Simplifying 41u = u2 + -5 Reorder the terms: 41u = -5 + u2 Solving 41u = -5 + u2 Solving for variable 'u'. Reorder the terms: 5 + 41u + -1u2 = -5 + u2 + 5 + -1u2 Reorder the terms: 5 + 41u + -1u2 = -5 + 5 + u2 + -1u2 Combine like terms: -5 + 5 = 0 5 + 41u + -1u2 = 0 + u2 + -1u2 5 + 41u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 5 + 41u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -41u + u2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -41u + 5 + u2 = 0 + 5 Reorder the terms: -5 + 5 + -41u + u2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -41u + u2 = 0 + 5 -41u + u2 = 0 + 5 Combine like terms: 0 + 5 = 5 -41u + u2 = 5 The u term is -41u. Take half its coefficient (-20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. -41u + 420.25 + u2 = 5 + 420.25 Reorder the terms: 420.25 + -41u + u2 = 5 + 420.25 Combine like terms: 5 + 420.25 = 425.25 420.25 + -41u + u2 = 425.25 Factor a perfect square on the left side: (u + -20.5)(u + -20.5) = 425.25 Calculate the square root of the right side: 20.621590627 Break this problem into two subproblems by setting (u + -20.5) equal to 20.621590627 and -20.621590627.Subproblem 1
u + -20.5 = 20.621590627 Simplifying u + -20.5 = 20.621590627 Reorder the terms: -20.5 + u = 20.621590627 Solving -20.5 + u = 20.621590627 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + u = 20.621590627 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + u = 20.621590627 + 20.5 u = 20.621590627 + 20.5 Combine like terms: 20.621590627 + 20.5 = 41.121590627 u = 41.121590627 Simplifying u = 41.121590627Subproblem 2
u + -20.5 = -20.621590627 Simplifying u + -20.5 = -20.621590627 Reorder the terms: -20.5 + u = -20.621590627 Solving -20.5 + u = -20.621590627 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + u = -20.621590627 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + u = -20.621590627 + 20.5 u = -20.621590627 + 20.5 Combine like terms: -20.621590627 + 20.5 = -0.121590627 u = -0.121590627 Simplifying u = -0.121590627Solution
The solution to the problem is based on the solutions from the subproblems. u = {41.121590627, -0.121590627}
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