r^2+6r+4=0

Solution for r^2+6r+4=0 equation:

Simplifying
r2 + 6r + 4 = 0

Reorder the terms:
4 + 6r + r2 = 0

Solving
4 + 6r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6r + -4 + r2 = 0 + -4

Reorder the terms:
4 + -4 + 6r + r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6r + r2 = 0 + -4
6r + r2 = 0 + -4

Combine like terms: 0 + -4 = -4
6r + r2 = -4

The r term is 6r.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6r + 9 + r2 = -4 + 9

Reorder the terms:
9 + 6r + r2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + 6r + r2 = 5

Factor a perfect square on the left side:
(r + 3)(r + 3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(r + 3) equal to 2.236067978 and -2.236067978.

Subproblem 1
r + 3 = 2.236067978

Simplifying
r + 3 = 2.236067978

Reorder the terms:
3 + r = 2.236067978

Solving
3 + r = 2.236067978

Solving for variable 'r'.

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

Add '-3' to each side of the equation.
3 + -3 + r = 2.236067978 + -3

Combine like terms: 3 + -3 = 0
0 + r = 2.236067978 + -3
r = 2.236067978 + -3

Combine like terms: 2.236067978 + -3 = -0.763932022
r = -0.763932022

Simplifying
r = -0.763932022

Subproblem 2
r + 3 = -2.236067978

Simplifying
r + 3 = -2.236067978

Reorder the terms:
3 + r = -2.236067978

Solving
3 + r = -2.236067978

Solving for variable 'r'.

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

Add '-3' to each side of the equation.
3 + -3 + r = -2.236067978 + -3

Combine like terms: 3 + -3 = 0
0 + r = -2.236067978 + -3
r = -2.236067978 + -3

Combine like terms: -2.236067978 + -3 = -5.236067978
r = -5.236067978

Simplifying
r = -5.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.763932022, -5.236067978}