z^2-12z+26=0

Solution for z^2-12z+26=0 equation:

Simplifying
z2 + -12z + 26 = 0

Reorder the terms:
26 + -12z + z2 = 0

Solving
26 + -12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -12z + -26 + z2 = 0 + -26

Reorder the terms:
26 + -26 + -12z + z2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -12z + z2 = 0 + -26
-12z + z2 = 0 + -26

Combine like terms: 0 + -26 = -26
-12z + z2 = -26

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 = -26 + 36

Reorder the terms:
36 + -12z + z2 = -26 + 36

Combine like terms: -26 + 36 = 10
36 + -12z + z2 = 10

Factor a perfect square on the left side:
(z + -6)(z + -6) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(z + -6) equal to 3.16227766 and -3.16227766.

Subproblem 1
z + -6 = 3.16227766

Simplifying
z + -6 = 3.16227766

Reorder the terms:
-6 + z = 3.16227766

Solving
-6 + z = 3.16227766

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 = 3.16227766 + 6

Combine like terms: -6 + 6 = 0
0 + z = 3.16227766 + 6
z = 3.16227766 + 6

Combine like terms: 3.16227766 + 6 = 9.16227766
z = 9.16227766

Simplifying
z = 9.16227766

Subproblem 2
z + -6 = -3.16227766

Simplifying
z + -6 = -3.16227766

Reorder the terms:
-6 + z = -3.16227766

Solving
-6 + z = -3.16227766

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 = -3.16227766 + 6

Combine like terms: -6 + 6 = 0
0 + z = -3.16227766 + 6
z = -3.16227766 + 6

Combine like terms: -3.16227766 + 6 = 2.83772234
z = 2.83772234

Simplifying
z = 2.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {9.16227766, 2.83772234}