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Simplifying u2 + -9 = 2u2 + -11u + 3 Reorder the terms: -9 + u2 = 2u2 + -11u + 3 Reorder the terms: -9 + u2 = 3 + -11u + 2u2 Solving -9 + u2 = 3 + -11u + 2u2 Solving for variable 'u'. Reorder the terms: -9 + -3 + 11u + u2 + -2u2 = 3 + -11u + 2u2 + -3 + 11u + -2u2 Combine like terms: -9 + -3 = -12 -12 + 11u + u2 + -2u2 = 3 + -11u + 2u2 + -3 + 11u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -12 + 11u + -1u2 = 3 + -11u + 2u2 + -3 + 11u + -2u2 Reorder the terms: -12 + 11u + -1u2 = 3 + -3 + -11u + 11u + 2u2 + -2u2 Combine like terms: 3 + -3 = 0 -12 + 11u + -1u2 = 0 + -11u + 11u + 2u2 + -2u2 -12 + 11u + -1u2 = -11u + 11u + 2u2 + -2u2 Combine like terms: -11u + 11u = 0 -12 + 11u + -1u2 = 0 + 2u2 + -2u2 -12 + 11u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -12 + 11u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -11u + u2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -11u + -12 + u2 = 0 + -12 Reorder the terms: 12 + -12 + -11u + u2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -11u + u2 = 0 + -12 -11u + u2 = 0 + -12 Combine like terms: 0 + -12 = -12 -11u + u2 = -12 The u term is -11u. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11u + 30.25 + u2 = -12 + 30.25 Reorder the terms: 30.25 + -11u + u2 = -12 + 30.25 Combine like terms: -12 + 30.25 = 18.25 30.25 + -11u + u2 = 18.25 Factor a perfect square on the left side: (u + -5.5)(u + -5.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (u + -5.5) equal to 4.272001873 and -4.272001873.Subproblem 1
u + -5.5 = 4.272001873 Simplifying u + -5.5 = 4.272001873 Reorder the terms: -5.5 + u = 4.272001873 Solving -5.5 + u = 4.272001873 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + u = 4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + u = 4.272001873 + 5.5 u = 4.272001873 + 5.5 Combine like terms: 4.272001873 + 5.5 = 9.772001873 u = 9.772001873 Simplifying u = 9.772001873Subproblem 2
u + -5.5 = -4.272001873 Simplifying u + -5.5 = -4.272001873 Reorder the terms: -5.5 + u = -4.272001873 Solving -5.5 + u = -4.272001873 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + u = -4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + u = -4.272001873 + 5.5 u = -4.272001873 + 5.5 Combine like terms: -4.272001873 + 5.5 = 1.227998127 u = 1.227998127 Simplifying u = 1.227998127Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.772001873, 1.227998127}
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