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Simplifying u2 + 16u = 1 Reorder the terms: 16u + u2 = 1 Solving 16u + u2 = 1 Solving for variable 'u'. Reorder the terms: -1 + 16u + u2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 16u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 16u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + 16u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 16u + u2 = 0 + 1 16u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 16u + u2 = 1 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 = 1 + 64 Reorder the terms: 64 + 16u + u2 = 1 + 64 Combine like terms: 1 + 64 = 65 64 + 16u + u2 = 65 Factor a perfect square on the left side: (u + 8)(u + 8) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (u + 8) equal to 8.062257748 and -8.062257748.Subproblem 1
u + 8 = 8.062257748 Simplifying u + 8 = 8.062257748 Reorder the terms: 8 + u = 8.062257748 Solving 8 + u = 8.062257748 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 = 8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + u = 8.062257748 + -8 u = 8.062257748 + -8 Combine like terms: 8.062257748 + -8 = 0.062257748 u = 0.062257748 Simplifying u = 0.062257748Subproblem 2
u + 8 = -8.062257748 Simplifying u + 8 = -8.062257748 Reorder the terms: 8 + u = -8.062257748 Solving 8 + u = -8.062257748 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 = -8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + u = -8.062257748 + -8 u = -8.062257748 + -8 Combine like terms: -8.062257748 + -8 = -16.062257748 u = -16.062257748 Simplifying u = -16.062257748Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.062257748, -16.062257748}
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