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Simplifying u2 + 11u + -28 = 0 Reorder the terms: -28 + 11u + u2 = 0 Solving -28 + 11u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 11u + 28 + u2 = 0 + 28 Reorder the terms: -28 + 28 + 11u + u2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 11u + u2 = 0 + 28 11u + u2 = 0 + 28 Combine like terms: 0 + 28 = 28 11u + u2 = 28 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 = 28 + 30.25 Reorder the terms: 30.25 + 11u + u2 = 28 + 30.25 Combine like terms: 28 + 30.25 = 58.25 30.25 + 11u + u2 = 58.25 Factor a perfect square on the left side: (u + 5.5)(u + 5.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (u + 5.5) equal to 7.632168761 and -7.632168761.Subproblem 1
u + 5.5 = 7.632168761 Simplifying u + 5.5 = 7.632168761 Reorder the terms: 5.5 + u = 7.632168761 Solving 5.5 + u = 7.632168761 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 = 7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + u = 7.632168761 + -5.5 u = 7.632168761 + -5.5 Combine like terms: 7.632168761 + -5.5 = 2.132168761 u = 2.132168761 Simplifying u = 2.132168761Subproblem 2
u + 5.5 = -7.632168761 Simplifying u + 5.5 = -7.632168761 Reorder the terms: 5.5 + u = -7.632168761 Solving 5.5 + u = -7.632168761 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 = -7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + u = -7.632168761 + -5.5 u = -7.632168761 + -5.5 Combine like terms: -7.632168761 + -5.5 = -13.132168761 u = -13.132168761 Simplifying u = -13.132168761Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.132168761, -13.132168761}
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