z^2+12z+14=0

Solution for z^2+12z+14=0 equation:

Simplifying
z2 + 12z + 14 = 0

Reorder the terms:
14 + 12z + z2 = 0

Solving
14 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 12z + -14 + z2 = 0 + -14

Reorder the terms:
14 + -14 + 12z + z2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 12z + z2 = 0 + -14
12z + z2 = 0 + -14

Combine like terms: 0 + -14 = -14
12z + z2 = -14

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 = -14 + 36

Reorder the terms:
36 + 12z + z2 = -14 + 36

Combine like terms: -14 + 36 = 22
36 + 12z + z2 = 22

Factor a perfect square on the left side:
(z + 6)(z + 6) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(z + 6) equal to 4.69041576 and -4.69041576.

Subproblem 1
z + 6 = 4.69041576

Simplifying
z + 6 = 4.69041576

Reorder the terms:
6 + z = 4.69041576

Solving
6 + z = 4.69041576

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 = 4.69041576 + -6

Combine like terms: 6 + -6 = 0
0 + z = 4.69041576 + -6
z = 4.69041576 + -6

Combine like terms: 4.69041576 + -6 = -1.30958424
z = -1.30958424

Simplifying
z = -1.30958424

Subproblem 2
z + 6 = -4.69041576

Simplifying
z + 6 = -4.69041576

Reorder the terms:
6 + z = -4.69041576

Solving
6 + z = -4.69041576

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 = -4.69041576 + -6

Combine like terms: 6 + -6 = 0
0 + z = -4.69041576 + -6
z = -4.69041576 + -6

Combine like terms: -4.69041576 + -6 = -10.69041576
z = -10.69041576

Simplifying
z = -10.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-1.30958424, -10.69041576}