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Simplifying u2 + 6u + -122 = 0 Reorder the terms: -122 + 6u + u2 = 0 Solving -122 + 6u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + 6u + 122 + u2 = 0 + 122 Reorder the terms: -122 + 122 + 6u + u2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + 6u + u2 = 0 + 122 6u + u2 = 0 + 122 Combine like terms: 0 + 122 = 122 6u + u2 = 122 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = 122 + 9 Reorder the terms: 9 + 6u + u2 = 122 + 9 Combine like terms: 122 + 9 = 131 9 + 6u + u2 = 131 Factor a perfect square on the left side: (u + 3)(u + 3) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (u + 3) equal to 11.445523142 and -11.445523142.Subproblem 1
u + 3 = 11.445523142 Simplifying u + 3 = 11.445523142 Reorder the terms: 3 + u = 11.445523142 Solving 3 + u = 11.445523142 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 11.445523142 + -3 Combine like terms: 3 + -3 = 0 0 + u = 11.445523142 + -3 u = 11.445523142 + -3 Combine like terms: 11.445523142 + -3 = 8.445523142 u = 8.445523142 Simplifying u = 8.445523142Subproblem 2
u + 3 = -11.445523142 Simplifying u + 3 = -11.445523142 Reorder the terms: 3 + u = -11.445523142 Solving 3 + u = -11.445523142 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -11.445523142 + -3 Combine like terms: 3 + -3 = 0 0 + u = -11.445523142 + -3 u = -11.445523142 + -3 Combine like terms: -11.445523142 + -3 = -14.445523142 u = -14.445523142 Simplifying u = -14.445523142Solution
The solution to the problem is based on the solutions from the subproblems. u = {8.445523142, -14.445523142}
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