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Simplifying 5 = u2 + 11u Reorder the terms: 5 = 11u + u2 Solving 5 = 11u + u2 Solving for variable 'u'. Reorder the terms: 5 + -11u + -1u2 = 11u + -11u + u2 + -1u2 Combine like terms: 11u + -11u = 0 5 + -11u + -1u2 = 0 + u2 + -1u2 5 + -11u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 5 + -11u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 11u + u2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 11u + 5 + u2 = 0 + 5 Reorder the terms: -5 + 5 + 11u + u2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 11u + u2 = 0 + 5 11u + u2 = 0 + 5 Combine like terms: 0 + 5 = 5 11u + u2 = 5 The u term is 11u. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11u + 30.25 + u2 = 5 + 30.25 Reorder the terms: 30.25 + 11u + u2 = 5 + 30.25 Combine like terms: 5 + 30.25 = 35.25 30.25 + 11u + u2 = 35.25 Factor a perfect square on the left side: (u + 5.5)(u + 5.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (u + 5.5) equal to 5.937171044 and -5.937171044.Subproblem 1
u + 5.5 = 5.937171044 Simplifying u + 5.5 = 5.937171044 Reorder the terms: 5.5 + u = 5.937171044 Solving 5.5 + u = 5.937171044 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + u = 5.937171044 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + u = 5.937171044 + -5.5 u = 5.937171044 + -5.5 Combine like terms: 5.937171044 + -5.5 = 0.437171044 u = 0.437171044 Simplifying u = 0.437171044Subproblem 2
u + 5.5 = -5.937171044 Simplifying u + 5.5 = -5.937171044 Reorder the terms: 5.5 + u = -5.937171044 Solving 5.5 + u = -5.937171044 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + u = -5.937171044 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + u = -5.937171044 + -5.5 u = -5.937171044 + -5.5 Combine like terms: -5.937171044 + -5.5 = -11.437171044 u = -11.437171044 Simplifying u = -11.437171044Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.437171044, -11.437171044}
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