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Simplifying u2 + -5u + -11 = 0 Reorder the terms: -11 + -5u + u2 = 0 Solving -11 + -5u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -5u + 11 + u2 = 0 + 11 Reorder the terms: -11 + 11 + -5u + u2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -5u + u2 = 0 + 11 -5u + u2 = 0 + 11 Combine like terms: 0 + 11 = 11 -5u + u2 = 11 The u term is -5u. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5u + 6.25 + u2 = 11 + 6.25 Reorder the terms: 6.25 + -5u + u2 = 11 + 6.25 Combine like terms: 11 + 6.25 = 17.25 6.25 + -5u + u2 = 17.25 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (u + -2.5) equal to 4.153311931 and -4.153311931.Subproblem 1
u + -2.5 = 4.153311931 Simplifying u + -2.5 = 4.153311931 Reorder the terms: -2.5 + u = 4.153311931 Solving -2.5 + u = 4.153311931 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + u = 4.153311931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 4.153311931 + 2.5 u = 4.153311931 + 2.5 Combine like terms: 4.153311931 + 2.5 = 6.653311931 u = 6.653311931 Simplifying u = 6.653311931Subproblem 2
u + -2.5 = -4.153311931 Simplifying u + -2.5 = -4.153311931 Reorder the terms: -2.5 + u = -4.153311931 Solving -2.5 + u = -4.153311931 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + u = -4.153311931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -4.153311931 + 2.5 u = -4.153311931 + 2.5 Combine like terms: -4.153311931 + 2.5 = -1.653311931 u = -1.653311931 Simplifying u = -1.653311931Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.653311931, -1.653311931}
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