z^2+12z+5=0

Solution for z^2+12z+5=0 equation:

Simplifying
z2 + 12z + 5 = 0

Reorder the terms:
5 + 12z + z2 = 0

Solving
5 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 12z + -5 + z2 = 0 + -5

Reorder the terms:
5 + -5 + 12z + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 12z + z2 = 0 + -5
12z + z2 = 0 + -5

Combine like terms: 0 + -5 = -5
12z + z2 = -5

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

Add '36' to each side of the equation.
12z + 36 + z2 = -5 + 36

Reorder the terms:
36 + 12z + z2 = -5 + 36

Combine like terms: -5 + 36 = 31
36 + 12z + z2 = 31

Factor a perfect square on the left side:
(z + 6)(z + 6) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(z + 6) equal to 5.567764363 and -5.567764363.

Subproblem 1
z + 6 = 5.567764363

Simplifying
z + 6 = 5.567764363

Reorder the terms:
6 + z = 5.567764363

Solving
6 + z = 5.567764363

Solving for variable 'z'.

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

Add '-6' to each side of the equation.
6 + -6 + z = 5.567764363 + -6

Combine like terms: 6 + -6 = 0
0 + z = 5.567764363 + -6
z = 5.567764363 + -6

Combine like terms: 5.567764363 + -6 = -0.432235637
z = -0.432235637

Simplifying
z = -0.432235637

Subproblem 2
z + 6 = -5.567764363

Simplifying
z + 6 = -5.567764363

Reorder the terms:
6 + z = -5.567764363

Solving
6 + z = -5.567764363

Solving for variable 'z'.

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

Add '-6' to each side of the equation.
6 + -6 + z = -5.567764363 + -6

Combine like terms: 6 + -6 = 0
0 + z = -5.567764363 + -6
z = -5.567764363 + -6

Combine like terms: -5.567764363 + -6 = -11.567764363
z = -11.567764363

Simplifying
z = -11.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-0.432235637, -11.567764363}