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Simplifying u2 + 10u + -2 = 0 Reorder the terms: -2 + 10u + u2 = 0 Solving -2 + 10u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 10u + 2 + u2 = 0 + 2 Reorder the terms: -2 + 2 + 10u + u2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 10u + u2 = 0 + 2 10u + u2 = 0 + 2 Combine like terms: 0 + 2 = 2 10u + u2 = 2 The u term is 10u. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10u + 25 + u2 = 2 + 25 Reorder the terms: 25 + 10u + u2 = 2 + 25 Combine like terms: 2 + 25 = 27 25 + 10u + u2 = 27 Factor a perfect square on the left side: (u + 5)(u + 5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (u + 5) equal to 5.196152423 and -5.196152423.Subproblem 1
u + 5 = 5.196152423 Simplifying u + 5 = 5.196152423 Reorder the terms: 5 + u = 5.196152423 Solving 5 + u = 5.196152423 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = 5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + u = 5.196152423 + -5 u = 5.196152423 + -5 Combine like terms: 5.196152423 + -5 = 0.196152423 u = 0.196152423 Simplifying u = 0.196152423Subproblem 2
u + 5 = -5.196152423 Simplifying u + 5 = -5.196152423 Reorder the terms: 5 + u = -5.196152423 Solving 5 + u = -5.196152423 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = -5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + u = -5.196152423 + -5 u = -5.196152423 + -5 Combine like terms: -5.196152423 + -5 = -10.196152423 u = -10.196152423 Simplifying u = -10.196152423Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.196152423, -10.196152423}
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