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Simplifying 2u2 + 11u + -5 = u2 + 9 Reorder the terms: -5 + 11u + 2u2 = u2 + 9 Reorder the terms: -5 + 11u + 2u2 = 9 + u2 Solving -5 + 11u + 2u2 = 9 + u2 Solving for variable 'u'. Reorder the terms: -5 + -9 + 11u + 2u2 + -1u2 = 9 + u2 + -9 + -1u2 Combine like terms: -5 + -9 = -14 -14 + 11u + 2u2 + -1u2 = 9 + u2 + -9 + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 -14 + 11u + 1u2 = 9 + u2 + -9 + -1u2 Reorder the terms: -14 + 11u + 1u2 = 9 + -9 + u2 + -1u2 Combine like terms: 9 + -9 = 0 -14 + 11u + 1u2 = 0 + u2 + -1u2 -14 + 11u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -14 + 11u + 1u2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 11u + 14 + u2 = 0 + 14 Reorder the terms: -14 + 14 + 11u + u2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 11u + u2 = 0 + 14 11u + u2 = 0 + 14 Combine like terms: 0 + 14 = 14 11u + u2 = 14 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 = 14 + 30.25 Reorder the terms: 30.25 + 11u + u2 = 14 + 30.25 Combine like terms: 14 + 30.25 = 44.25 30.25 + 11u + u2 = 44.25 Factor a perfect square on the left side: (u + 5.5)(u + 5.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (u + 5.5) equal to 6.652067348 and -6.652067348.Subproblem 1
u + 5.5 = 6.652067348 Simplifying u + 5.5 = 6.652067348 Reorder the terms: 5.5 + u = 6.652067348 Solving 5.5 + u = 6.652067348 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 = 6.652067348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + u = 6.652067348 + -5.5 u = 6.652067348 + -5.5 Combine like terms: 6.652067348 + -5.5 = 1.152067348 u = 1.152067348 Simplifying u = 1.152067348Subproblem 2
u + 5.5 = -6.652067348 Simplifying u + 5.5 = -6.652067348 Reorder the terms: 5.5 + u = -6.652067348 Solving 5.5 + u = -6.652067348 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 = -6.652067348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + u = -6.652067348 + -5.5 u = -6.652067348 + -5.5 Combine like terms: -6.652067348 + -5.5 = -12.152067348 u = -12.152067348 Simplifying u = -12.152067348Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.152067348, -12.152067348}
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