u^2-2u-2=0

Solution for u^2-2u-2=0 equation:

Simplifying
u2 + -2u + -2 = 0

Reorder the terms:
-2 + -2u + u2 = 0

Solving
-2 + -2u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2u + 2 + u2 = 0 + 2

Reorder the terms:
-2 + 2 + -2u + u2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2u + u2 = 0 + 2
-2u + u2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2u + u2 = 2

The u term is -2u.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2u + 1 + u2 = 2 + 1

Reorder the terms:
1 + -2u + u2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + -2u + u2 = 3

Factor a perfect square on the left side:
(u + -1)(u + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(u + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
u + -1 = 1.732050808

Simplifying
u + -1 = 1.732050808

Reorder the terms:
-1 + u = 1.732050808

Solving
-1 + u = 1.732050808

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + u = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + u = 1.732050808 + 1
u = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
u = 2.732050808

Simplifying
u = 2.732050808

Subproblem 2
u + -1 = -1.732050808

Simplifying
u + -1 = -1.732050808

Reorder the terms:
-1 + u = -1.732050808

Solving
-1 + u = -1.732050808

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + u = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + u = -1.732050808 + 1
u = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
u = -0.732050808

Simplifying
u = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.732050808, -0.732050808}