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Simplifying u2 + 22u + 27 = 0 Reorder the terms: 27 + 22u + u2 = 0 Solving 27 + 22u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 22u + -27 + u2 = 0 + -27 Reorder the terms: 27 + -27 + 22u + u2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 22u + u2 = 0 + -27 22u + u2 = 0 + -27 Combine like terms: 0 + -27 = -27 22u + u2 = -27 The u term is 22u. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22u + 121 + u2 = -27 + 121 Reorder the terms: 121 + 22u + u2 = -27 + 121 Combine like terms: -27 + 121 = 94 121 + 22u + u2 = 94 Factor a perfect square on the left side: (u + 11)(u + 11) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (u + 11) equal to 9.695359715 and -9.695359715.Subproblem 1
u + 11 = 9.695359715 Simplifying u + 11 = 9.695359715 Reorder the terms: 11 + u = 9.695359715 Solving 11 + u = 9.695359715 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + u = 9.695359715 + -11 Combine like terms: 11 + -11 = 0 0 + u = 9.695359715 + -11 u = 9.695359715 + -11 Combine like terms: 9.695359715 + -11 = -1.304640285 u = -1.304640285 Simplifying u = -1.304640285Subproblem 2
u + 11 = -9.695359715 Simplifying u + 11 = -9.695359715 Reorder the terms: 11 + u = -9.695359715 Solving 11 + u = -9.695359715 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + u = -9.695359715 + -11 Combine like terms: 11 + -11 = 0 0 + u = -9.695359715 + -11 u = -9.695359715 + -11 Combine like terms: -9.695359715 + -11 = -20.695359715 u = -20.695359715 Simplifying u = -20.695359715Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.304640285, -20.695359715}
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