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Simplifying u2 + -6u + 1 = 0 Reorder the terms: 1 + -6u + u2 = 0 Solving 1 + -6u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6u + -1 + u2 = 0 + -1 Reorder the terms: 1 + -1 + -6u + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6u + u2 = 0 + -1 -6u + u2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6u + u2 = -1 The u term is -6u. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6u + 9 + u2 = -1 + 9 Reorder the terms: 9 + -6u + u2 = -1 + 9 Combine like terms: -1 + 9 = 8 9 + -6u + u2 = 8 Factor a perfect square on the left side: (u + -3)(u + -3) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (u + -3) equal to 2.828427125 and -2.828427125.Subproblem 1
u + -3 = 2.828427125 Simplifying u + -3 = 2.828427125 Reorder the terms: -3 + u = 2.828427125 Solving -3 + u = 2.828427125 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + u = 2.828427125 + 3 u = 2.828427125 + 3 Combine like terms: 2.828427125 + 3 = 5.828427125 u = 5.828427125 Simplifying u = 5.828427125Subproblem 2
u + -3 = -2.828427125 Simplifying u + -3 = -2.828427125 Reorder the terms: -3 + u = -2.828427125 Solving -3 + u = -2.828427125 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = -2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + u = -2.828427125 + 3 u = -2.828427125 + 3 Combine like terms: -2.828427125 + 3 = 0.171572875 u = 0.171572875 Simplifying u = 0.171572875Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.828427125, 0.171572875}
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