r^2+4r+2=0

Solution for r^2+4r+2=0 equation:

Simplifying
r2 + 4r + 2 = 0

Reorder the terms:
2 + 4r + r2 = 0

Solving
2 + 4r + 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 + 4r + -2 + r2 = 0 + -2

Reorder the terms:
2 + -2 + 4r + r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4r + r2 = 0 + -2
4r + r2 = 0 + -2

Combine like terms: 0 + -2 = -2
4r + r2 = -2

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = -2 + 4

Reorder the terms:
4 + 4r + r2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + 4r + r2 = 2

Factor a perfect square on the left side:
(r + 2)(r + 2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(r + 2) equal to 1.414213562 and -1.414213562.

Subproblem 1
r + 2 = 1.414213562

Simplifying
r + 2 = 1.414213562

Reorder the terms:
2 + r = 1.414213562

Solving
2 + r = 1.414213562

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = 1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + r = 1.414213562 + -2
r = 1.414213562 + -2

Combine like terms: 1.414213562 + -2 = -0.585786438
r = -0.585786438

Simplifying
r = -0.585786438

Subproblem 2
r + 2 = -1.414213562

Simplifying
r + 2 = -1.414213562

Reorder the terms:
2 + r = -1.414213562

Solving
2 + r = -1.414213562

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = -1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + r = -1.414213562 + -2
r = -1.414213562 + -2

Combine like terms: -1.414213562 + -2 = -3.414213562
r = -3.414213562

Simplifying
r = -3.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.585786438, -3.414213562}