z^2+12z-1=0

Solution for z^2+12z-1=0 equation:

Simplifying
z2 + 12z + -1 = 0

Reorder the terms:
-1 + 12z + z2 = 0

Solving
-1 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 12z + 1 + z2 = 0 + 1

Reorder the terms:
-1 + 1 + 12z + z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 12z + z2 = 0 + 1
12z + z2 = 0 + 1

Combine like terms: 0 + 1 = 1
12z + z2 = 1

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 = 1 + 36

Reorder the terms:
36 + 12z + z2 = 1 + 36

Combine like terms: 1 + 36 = 37
36 + 12z + z2 = 37

Factor a perfect square on the left side:
(z + 6)(z + 6) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(z + 6) equal to 6.08276253 and -6.08276253.

Subproblem 1
z + 6 = 6.08276253

Simplifying
z + 6 = 6.08276253

Reorder the terms:
6 + z = 6.08276253

Solving
6 + z = 6.08276253

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 = 6.08276253 + -6

Combine like terms: 6 + -6 = 0
0 + z = 6.08276253 + -6
z = 6.08276253 + -6

Combine like terms: 6.08276253 + -6 = 0.08276253
z = 0.08276253

Simplifying
z = 0.08276253

Subproblem 2
z + 6 = -6.08276253

Simplifying
z + 6 = -6.08276253

Reorder the terms:
6 + z = -6.08276253

Solving
6 + z = -6.08276253

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 = -6.08276253 + -6

Combine like terms: 6 + -6 = 0
0 + z = -6.08276253 + -6
z = -6.08276253 + -6

Combine like terms: -6.08276253 + -6 = -12.08276253
z = -12.08276253

Simplifying
z = -12.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.08276253, -12.08276253}