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Simplifying u2 + 8u = 23 Reorder the terms: 8u + u2 = 23 Solving 8u + u2 = 23 Solving for variable 'u'. Reorder the terms: -23 + 8u + u2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 8u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 8u + 23 + u2 = 0 + 23 Reorder the terms: -23 + 23 + 8u + u2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 8u + u2 = 0 + 23 8u + u2 = 0 + 23 Combine like terms: 0 + 23 = 23 8u + u2 = 23 The u term is 8u. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8u + 16 + u2 = 23 + 16 Reorder the terms: 16 + 8u + u2 = 23 + 16 Combine like terms: 23 + 16 = 39 16 + 8u + u2 = 39 Factor a perfect square on the left side: (u + 4)(u + 4) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (u + 4) equal to 6.244997998 and -6.244997998.Subproblem 1
u + 4 = 6.244997998 Simplifying u + 4 = 6.244997998 Reorder the terms: 4 + u = 6.244997998 Solving 4 + u = 6.244997998 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + u = 6.244997998 + -4 Combine like terms: 4 + -4 = 0 0 + u = 6.244997998 + -4 u = 6.244997998 + -4 Combine like terms: 6.244997998 + -4 = 2.244997998 u = 2.244997998 Simplifying u = 2.244997998Subproblem 2
u + 4 = -6.244997998 Simplifying u + 4 = -6.244997998 Reorder the terms: 4 + u = -6.244997998 Solving 4 + u = -6.244997998 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + u = -6.244997998 + -4 Combine like terms: 4 + -4 = 0 0 + u = -6.244997998 + -4 u = -6.244997998 + -4 Combine like terms: -6.244997998 + -4 = -10.244997998 u = -10.244997998 Simplifying u = -10.244997998Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.244997998, -10.244997998}
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