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Simplifying u2 + 8u + 8 = 0 Reorder the terms: 8 + 8u + u2 = 0 Solving 8 + 8u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 8u + -8 + u2 = 0 + -8 Reorder the terms: 8 + -8 + 8u + u2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 8u + u2 = 0 + -8 8u + u2 = 0 + -8 Combine like terms: 0 + -8 = -8 8u + u2 = -8 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 = -8 + 16 Reorder the terms: 16 + 8u + u2 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + 8u + u2 = 8 Factor a perfect square on the left side: (u + 4)(u + 4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (u + 4) equal to 2.828427125 and -2.828427125.Subproblem 1
u + 4 = 2.828427125 Simplifying u + 4 = 2.828427125 Reorder the terms: 4 + u = 2.828427125 Solving 4 + u = 2.828427125 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 = 2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + u = 2.828427125 + -4 u = 2.828427125 + -4 Combine like terms: 2.828427125 + -4 = -1.171572875 u = -1.171572875 Simplifying u = -1.171572875Subproblem 2
u + 4 = -2.828427125 Simplifying u + 4 = -2.828427125 Reorder the terms: 4 + u = -2.828427125 Solving 4 + u = -2.828427125 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 = -2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + u = -2.828427125 + -4 u = -2.828427125 + -4 Combine like terms: -2.828427125 + -4 = -6.828427125 u = -6.828427125 Simplifying u = -6.828427125Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.171572875, -6.828427125}
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