k^2+12k+6=0

Solution for k^2+12k+6=0 equation:

Simplifying
k2 + 12k + 6 = 0

Reorder the terms:
6 + 12k + k2 = 0

Solving
6 + 12k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 12k + -6 + k2 = 0 + -6

Reorder the terms:
6 + -6 + 12k + k2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12k + k2 = 0 + -6
12k + k2 = 0 + -6

Combine like terms: 0 + -6 = -6
12k + k2 = -6

The k term is 12k.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12k + 36 + k2 = -6 + 36

Reorder the terms:
36 + 12k + k2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + 12k + k2 = 30

Factor a perfect square on the left side:
(k + 6)(k + 6) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(k + 6) equal to 5.477225575 and -5.477225575.

Subproblem 1
k + 6 = 5.477225575

Simplifying
k + 6 = 5.477225575

Reorder the terms:
6 + k = 5.477225575

Solving
6 + k = 5.477225575

Solving for variable 'k'.

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

Add '-6' to each side of the equation.
6 + -6 + k = 5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + k = 5.477225575 + -6
k = 5.477225575 + -6

Combine like terms: 5.477225575 + -6 = -0.522774425
k = -0.522774425

Simplifying
k = -0.522774425

Subproblem 2
k + 6 = -5.477225575

Simplifying
k + 6 = -5.477225575

Reorder the terms:
6 + k = -5.477225575

Solving
6 + k = -5.477225575

Solving for variable 'k'.

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

Add '-6' to each side of the equation.
6 + -6 + k = -5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + k = -5.477225575 + -6
k = -5.477225575 + -6

Combine like terms: -5.477225575 + -6 = -11.477225575
k = -11.477225575

Simplifying
k = -11.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.522774425, -11.477225575}