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 = 35
36 + -12z + z2 = 35

Factor a perfect square on the left side:
(z + -6)(z + -6) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(z + -6) equal to 5.916079783 and -5.916079783.

Subproblem 1
z + -6 = 5.916079783

Simplifying
z + -6 = 5.916079783

Reorder the terms:
-6 + z = 5.916079783

Solving
-6 + z = 5.916079783

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 = 5.916079783 + 6

Combine like terms: -6 + 6 = 0
0 + z = 5.916079783 + 6
z = 5.916079783 + 6

Combine like terms: 5.916079783 + 6 = 11.916079783
z = 11.916079783

Simplifying
z = 11.916079783

Subproblem 2
z + -6 = -5.916079783

Simplifying
z + -6 = -5.916079783

Reorder the terms:
-6 + z = -5.916079783

Solving
-6 + z = -5.916079783

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 = -5.916079783 + 6

Combine like terms: -6 + 6 = 0
0 + z = -5.916079783 + 6
z = -5.916079783 + 6

Combine like terms: -5.916079783 + 6 = 0.083920217
z = 0.083920217

Simplifying
z = 0.083920217

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {11.916079783, 0.083920217}