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Simplifying u2 + 6u + 3u + 18 + u2 + 13u + 13 + -1u2 + -7u + -5u + -35 = 0 Reorder the terms: 18 + 13 + -35 + 6u + 3u + 13u + -7u + -5u + u2 + u2 + -1u2 = 0 Combine like terms: 18 + 13 = 31 31 + -35 + 6u + 3u + 13u + -7u + -5u + u2 + u2 + -1u2 = 0 Combine like terms: 31 + -35 = -4 -4 + 6u + 3u + 13u + -7u + -5u + u2 + u2 + -1u2 = 0 Combine like terms: 6u + 3u = 9u -4 + 9u + 13u + -7u + -5u + u2 + u2 + -1u2 = 0 Combine like terms: 9u + 13u = 22u -4 + 22u + -7u + -5u + u2 + u2 + -1u2 = 0 Combine like terms: 22u + -7u = 15u -4 + 15u + -5u + u2 + u2 + -1u2 = 0 Combine like terms: 15u + -5u = 10u -4 + 10u + u2 + u2 + -1u2 = 0 Combine like terms: u2 + u2 = 2u2 -4 + 10u + 2u2 + -1u2 = 0 Combine like terms: 2u2 + -1u2 = 1u2 -4 + 10u + 1u2 = 0 Solving -4 + 10u + 1u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 10u + 4 + u2 = 0 + 4 Reorder the terms: -4 + 4 + 10u + u2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 10u + u2 = 0 + 4 10u + u2 = 0 + 4 Combine like terms: 0 + 4 = 4 10u + u2 = 4 The u term is 10u. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10u + 25 + u2 = 4 + 25 Reorder the terms: 25 + 10u + u2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + 10u + u2 = 29 Factor a perfect square on the left side: (u + 5)(u + 5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (u + 5) equal to 5.385164807 and -5.385164807.Subproblem 1
u + 5 = 5.385164807 Simplifying u + 5 = 5.385164807 Reorder the terms: 5 + u = 5.385164807 Solving 5 + u = 5.385164807 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = 5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + u = 5.385164807 + -5 u = 5.385164807 + -5 Combine like terms: 5.385164807 + -5 = 0.385164807 u = 0.385164807 Simplifying u = 0.385164807Subproblem 2
u + 5 = -5.385164807 Simplifying u + 5 = -5.385164807 Reorder the terms: 5 + u = -5.385164807 Solving 5 + u = -5.385164807 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = -5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + u = -5.385164807 + -5 u = -5.385164807 + -5 Combine like terms: -5.385164807 + -5 = -10.385164807 u = -10.385164807 Simplifying u = -10.385164807Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.385164807, -10.385164807}
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