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Simplifying 6u2 + 11u + -27 = 0 Reorder the terms: -27 + 11u + 6u2 = 0 Solving -27 + 11u + 6u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.5 + 1.833333333u + u2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 1.833333333u + 4.5 + u2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 1.833333333u + u2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 1.833333333u + u2 = 0 + 4.5 1.833333333u + u2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 1.833333333u + u2 = 4.5 The u term is 1.833333333u. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333u + 0.8402777775 + u2 = 4.5 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333u + u2 = 4.5 + 0.8402777775 Combine like terms: 4.5 + 0.8402777775 = 5.3402777775 0.8402777775 + 1.833333333u + u2 = 5.3402777775 Factor a perfect square on the left side: (u + 0.9166666665)(u + 0.9166666665) = 5.3402777775 Calculate the square root of the right side: 2.310904104 Break this problem into two subproblems by setting (u + 0.9166666665) equal to 2.310904104 and -2.310904104.Subproblem 1
u + 0.9166666665 = 2.310904104 Simplifying u + 0.9166666665 = 2.310904104 Reorder the terms: 0.9166666665 + u = 2.310904104 Solving 0.9166666665 + u = 2.310904104 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + u = 2.310904104 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + u = 2.310904104 + -0.9166666665 u = 2.310904104 + -0.9166666665 Combine like terms: 2.310904104 + -0.9166666665 = 1.3942374375 u = 1.3942374375 Simplifying u = 1.3942374375Subproblem 2
u + 0.9166666665 = -2.310904104 Simplifying u + 0.9166666665 = -2.310904104 Reorder the terms: 0.9166666665 + u = -2.310904104 Solving 0.9166666665 + u = -2.310904104 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + u = -2.310904104 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + u = -2.310904104 + -0.9166666665 u = -2.310904104 + -0.9166666665 Combine like terms: -2.310904104 + -0.9166666665 = -3.2275707705 u = -3.2275707705 Simplifying u = -3.2275707705Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.3942374375, -3.2275707705}
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