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Simplifying u2 + 16u = -43 Reorder the terms: 16u + u2 = -43 Solving 16u + u2 = -43 Solving for variable 'u'. Reorder the terms: 43 + 16u + u2 = -43 + 43 Combine like terms: -43 + 43 = 0 43 + 16u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 16u + -43 + u2 = 0 + -43 Reorder the terms: 43 + -43 + 16u + u2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 16u + u2 = 0 + -43 16u + u2 = 0 + -43 Combine like terms: 0 + -43 = -43 16u + u2 = -43 The u term is 16u. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16u + 64 + u2 = -43 + 64 Reorder the terms: 64 + 16u + u2 = -43 + 64 Combine like terms: -43 + 64 = 21 64 + 16u + u2 = 21 Factor a perfect square on the left side: (u + 8)(u + 8) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (u + 8) equal to 4.582575695 and -4.582575695.Subproblem 1
u + 8 = 4.582575695 Simplifying u + 8 = 4.582575695 Reorder the terms: 8 + u = 4.582575695 Solving 8 + u = 4.582575695 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = 4.582575695 + -8 Combine like terms: 8 + -8 = 0 0 + u = 4.582575695 + -8 u = 4.582575695 + -8 Combine like terms: 4.582575695 + -8 = -3.417424305 u = -3.417424305 Simplifying u = -3.417424305Subproblem 2
u + 8 = -4.582575695 Simplifying u + 8 = -4.582575695 Reorder the terms: 8 + u = -4.582575695 Solving 8 + u = -4.582575695 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = -4.582575695 + -8 Combine like terms: 8 + -8 = 0 0 + u = -4.582575695 + -8 u = -4.582575695 + -8 Combine like terms: -4.582575695 + -8 = -12.582575695 u = -12.582575695 Simplifying u = -12.582575695Solution
The solution to the problem is based on the solutions from the subproblems. u = {-3.417424305, -12.582575695}
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