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Simplifying u2 + -6u + -39 = 0 Reorder the terms: -39 + -6u + u2 = 0 Solving -39 + -6u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -6u + 39 + u2 = 0 + 39 Reorder the terms: -39 + 39 + -6u + u2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -6u + u2 = 0 + 39 -6u + u2 = 0 + 39 Combine like terms: 0 + 39 = 39 -6u + u2 = 39 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 = 39 + 9 Reorder the terms: 9 + -6u + u2 = 39 + 9 Combine like terms: 39 + 9 = 48 9 + -6u + u2 = 48 Factor a perfect square on the left side: (u + -3)(u + -3) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (u + -3) equal to 6.92820323 and -6.92820323.Subproblem 1
u + -3 = 6.92820323 Simplifying u + -3 = 6.92820323 Reorder the terms: -3 + u = 6.92820323 Solving -3 + u = 6.92820323 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 = 6.92820323 + 3 Combine like terms: -3 + 3 = 0 0 + u = 6.92820323 + 3 u = 6.92820323 + 3 Combine like terms: 6.92820323 + 3 = 9.92820323 u = 9.92820323 Simplifying u = 9.92820323Subproblem 2
u + -3 = -6.92820323 Simplifying u + -3 = -6.92820323 Reorder the terms: -3 + u = -6.92820323 Solving -3 + u = -6.92820323 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 = -6.92820323 + 3 Combine like terms: -3 + 3 = 0 0 + u = -6.92820323 + 3 u = -6.92820323 + 3 Combine like terms: -6.92820323 + 3 = -3.92820323 u = -3.92820323 Simplifying u = -3.92820323Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.92820323, -3.92820323}
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