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Simplifying u2 + 4u + -43 = 0 Reorder the terms: -43 + 4u + u2 = 0 Solving -43 + 4u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 4u + 43 + u2 = 0 + 43 Reorder the terms: -43 + 43 + 4u + u2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 4u + u2 = 0 + 43 4u + u2 = 0 + 43 Combine like terms: 0 + 43 = 43 4u + u2 = 43 The u term is 4u. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4u + 4 + u2 = 43 + 4 Reorder the terms: 4 + 4u + u2 = 43 + 4 Combine like terms: 43 + 4 = 47 4 + 4u + u2 = 47 Factor a perfect square on the left side: (u + 2)(u + 2) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (u + 2) equal to 6.8556546 and -6.8556546.Subproblem 1
u + 2 = 6.8556546 Simplifying u + 2 = 6.8556546 Reorder the terms: 2 + u = 6.8556546 Solving 2 + u = 6.8556546 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = 6.8556546 + -2 Combine like terms: 2 + -2 = 0 0 + u = 6.8556546 + -2 u = 6.8556546 + -2 Combine like terms: 6.8556546 + -2 = 4.8556546 u = 4.8556546 Simplifying u = 4.8556546Subproblem 2
u + 2 = -6.8556546 Simplifying u + 2 = -6.8556546 Reorder the terms: 2 + u = -6.8556546 Solving 2 + u = -6.8556546 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = -6.8556546 + -2 Combine like terms: 2 + -2 = 0 0 + u = -6.8556546 + -2 u = -6.8556546 + -2 Combine like terms: -6.8556546 + -2 = -8.8556546 u = -8.8556546 Simplifying u = -8.8556546Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.8556546, -8.8556546}
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