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Simplifying 3u2 + 27u + 10 = 0 Reorder the terms: 10 + 27u + 3u2 = 0 Solving 10 + 27u + 3u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + 9u + u2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 9u + -3.333333333 + u2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 9u + u2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 9u + u2 = 0 + -3.333333333 9u + u2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 9u + u2 = -3.333333333 The u term is 9u. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9u + 20.25 + u2 = -3.333333333 + 20.25 Reorder the terms: 20.25 + 9u + u2 = -3.333333333 + 20.25 Combine like terms: -3.333333333 + 20.25 = 16.916666667 20.25 + 9u + u2 = 16.916666667 Factor a perfect square on the left side: (u + 4.5)(u + 4.5) = 16.916666667 Calculate the square root of the right side: 4.11298756 Break this problem into two subproblems by setting (u + 4.5) equal to 4.11298756 and -4.11298756.Subproblem 1
u + 4.5 = 4.11298756 Simplifying u + 4.5 = 4.11298756 Reorder the terms: 4.5 + u = 4.11298756 Solving 4.5 + u = 4.11298756 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = 4.11298756 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = 4.11298756 + -4.5 u = 4.11298756 + -4.5 Combine like terms: 4.11298756 + -4.5 = -0.38701244 u = -0.38701244 Simplifying u = -0.38701244Subproblem 2
u + 4.5 = -4.11298756 Simplifying u + 4.5 = -4.11298756 Reorder the terms: 4.5 + u = -4.11298756 Solving 4.5 + u = -4.11298756 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = -4.11298756 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = -4.11298756 + -4.5 u = -4.11298756 + -4.5 Combine like terms: -4.11298756 + -4.5 = -8.61298756 u = -8.61298756 Simplifying u = -8.61298756Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.38701244, -8.61298756}
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