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Simplifying u2 + 16u + 36 = 0 Reorder the terms: 36 + 16u + u2 = 0 Solving 36 + 16u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 16u + -36 + u2 = 0 + -36 Reorder the terms: 36 + -36 + 16u + u2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 16u + u2 = 0 + -36 16u + u2 = 0 + -36 Combine like terms: 0 + -36 = -36 16u + u2 = -36 The u term is 16u. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16u + 64 + u2 = -36 + 64 Reorder the terms: 64 + 16u + u2 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + 16u + u2 = 28 Factor a perfect square on the left side: (u + 8)(u + 8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (u + 8) equal to 5.291502622 and -5.291502622.Subproblem 1
u + 8 = 5.291502622 Simplifying u + 8 = 5.291502622 Reorder the terms: 8 + u = 5.291502622 Solving 8 + u = 5.291502622 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = 5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + u = 5.291502622 + -8 u = 5.291502622 + -8 Combine like terms: 5.291502622 + -8 = -2.708497378 u = -2.708497378 Simplifying u = -2.708497378Subproblem 2
u + 8 = -5.291502622 Simplifying u + 8 = -5.291502622 Reorder the terms: 8 + u = -5.291502622 Solving 8 + u = -5.291502622 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = -5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + u = -5.291502622 + -8 u = -5.291502622 + -8 Combine like terms: -5.291502622 + -8 = -13.291502622 u = -13.291502622 Simplifying u = -13.291502622Solution
The solution to the problem is based on the solutions from the subproblems. u = {-2.708497378, -13.291502622}
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