a^2-2a-2=0

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

Simplifying
a2 + -2a + -2 = 0

Reorder the terms:
-2 + -2a + a2 = 0

Solving
-2 + -2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + -2a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2a + a2 = 0 + 2
-2a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2a + a2 = 2

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

Add '1' to each side of the equation.
-2a + 1 + a2 = 2 + 1

Reorder the terms:
1 + -2a + a2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + -2a + a2 = 3

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

Calculate the square root of the right side: 1.732050808

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

Subproblem 1
a + -1 = 1.732050808

Simplifying
a + -1 = 1.732050808

Reorder the terms:
-1 + a = 1.732050808

Solving
-1 + a = 1.732050808

Solving for variable 'a'.

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

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

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

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

Simplifying
a = 2.732050808

Subproblem 2
a + -1 = -1.732050808

Simplifying
a + -1 = -1.732050808

Reorder the terms:
-1 + a = -1.732050808

Solving
-1 + a = -1.732050808

Solving for variable 'a'.

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

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

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

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

Simplifying
a = -0.732050808

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