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Simplifying 6u2 + 35u + 6 = 0 Reorder the terms: 6 + 35u + 6u2 = 0 Solving 6 + 35u + 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'. 1 + 5.833333333u + u2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5.833333333u + -1 + u2 = 0 + -1 Reorder the terms: 1 + -1 + 5.833333333u + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5.833333333u + u2 = 0 + -1 5.833333333u + u2 = 0 + -1 Combine like terms: 0 + -1 = -1 5.833333333u + u2 = -1 The u term is 5.833333333u. Take half its coefficient (2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. 5.833333333u + 8.506944446 + u2 = -1 + 8.506944446 Reorder the terms: 8.506944446 + 5.833333333u + u2 = -1 + 8.506944446 Combine like terms: -1 + 8.506944446 = 7.506944446 8.506944446 + 5.833333333u + u2 = 7.506944446 Factor a perfect square on the left side: (u + 2.916666667)(u + 2.916666667) = 7.506944446 Calculate the square root of the right side: 2.739880371 Break this problem into two subproblems by setting (u + 2.916666667) equal to 2.739880371 and -2.739880371.Subproblem 1
u + 2.916666667 = 2.739880371 Simplifying u + 2.916666667 = 2.739880371 Reorder the terms: 2.916666667 + u = 2.739880371 Solving 2.916666667 + u = 2.739880371 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + u = 2.739880371 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + u = 2.739880371 + -2.916666667 u = 2.739880371 + -2.916666667 Combine like terms: 2.739880371 + -2.916666667 = -0.176786296 u = -0.176786296 Simplifying u = -0.176786296Subproblem 2
u + 2.916666667 = -2.739880371 Simplifying u + 2.916666667 = -2.739880371 Reorder the terms: 2.916666667 + u = -2.739880371 Solving 2.916666667 + u = -2.739880371 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + u = -2.739880371 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + u = -2.739880371 + -2.916666667 u = -2.739880371 + -2.916666667 Combine like terms: -2.739880371 + -2.916666667 = -5.656547038 u = -5.656547038 Simplifying u = -5.656547038Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.176786296, -5.656547038}
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