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Simplifying 2u2 + 12u + 17 = u2 + 9 Reorder the terms: 17 + 12u + 2u2 = u2 + 9 Reorder the terms: 17 + 12u + 2u2 = 9 + u2 Solving 17 + 12u + 2u2 = 9 + u2 Solving for variable 'u'. Reorder the terms: 17 + -9 + 12u + 2u2 + -1u2 = 9 + u2 + -9 + -1u2 Combine like terms: 17 + -9 = 8 8 + 12u + 2u2 + -1u2 = 9 + u2 + -9 + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 8 + 12u + 1u2 = 9 + u2 + -9 + -1u2 Reorder the terms: 8 + 12u + 1u2 = 9 + -9 + u2 + -1u2 Combine like terms: 9 + -9 = 0 8 + 12u + 1u2 = 0 + u2 + -1u2 8 + 12u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 8 + 12u + 1u2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 12u + -8 + u2 = 0 + -8 Reorder the terms: 8 + -8 + 12u + u2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 12u + u2 = 0 + -8 12u + u2 = 0 + -8 Combine like terms: 0 + -8 = -8 12u + u2 = -8 The u term is 12u. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12u + 36 + u2 = -8 + 36 Reorder the terms: 36 + 12u + u2 = -8 + 36 Combine like terms: -8 + 36 = 28 36 + 12u + u2 = 28 Factor a perfect square on the left side: (u + 6)(u + 6) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (u + 6) equal to 5.291502622 and -5.291502622.Subproblem 1
u + 6 = 5.291502622 Simplifying u + 6 = 5.291502622 Reorder the terms: 6 + u = 5.291502622 Solving 6 + u = 5.291502622 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + u = 5.291502622 + -6 Combine like terms: 6 + -6 = 0 0 + u = 5.291502622 + -6 u = 5.291502622 + -6 Combine like terms: 5.291502622 + -6 = -0.708497378 u = -0.708497378 Simplifying u = -0.708497378Subproblem 2
u + 6 = -5.291502622 Simplifying u + 6 = -5.291502622 Reorder the terms: 6 + u = -5.291502622 Solving 6 + u = -5.291502622 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + u = -5.291502622 + -6 Combine like terms: 6 + -6 = 0 0 + u = -5.291502622 + -6 u = -5.291502622 + -6 Combine like terms: -5.291502622 + -6 = -11.291502622 u = -11.291502622 Simplifying u = -11.291502622Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.708497378, -11.291502622}
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