r^2+2r-2=0

Solution for r^2+2r-2=0 equation:

Simplifying
r2 + 2r + -2 = 0

Reorder the terms:
-2 + 2r + r2 = 0

Solving
-2 + 2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + 2r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2r + r2 = 0 + 2
2r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
2r + r2 = 2

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

Add '1' to each side of the equation.
2r + 1 + r2 = 2 + 1

Reorder the terms:
1 + 2r + r2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + 2r + r2 = 3

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

Calculate the square root of the right side: 1.732050808

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

Subproblem 1
r + 1 = 1.732050808

Simplifying
r + 1 = 1.732050808

Reorder the terms:
1 + r = 1.732050808

Solving
1 + r = 1.732050808

Solving for variable 'r'.

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

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

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

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

Simplifying
r = 0.732050808

Subproblem 2
r + 1 = -1.732050808

Simplifying
r + 1 = -1.732050808

Reorder the terms:
1 + r = -1.732050808

Solving
1 + r = -1.732050808

Solving for variable 'r'.

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

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

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

Combine like terms: -1.732050808 + -1 = -2.732050808
r = -2.732050808

Simplifying
r = -2.732050808

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