z^2-2z+1=323

Solution for z^2-2z+1=323 equation:

Simplifying
z2 + -2z + 1 = 323

Reorder the terms:
1 + -2z + z2 = 323

Solving
1 + -2z + z2 = 323

Solving for variable 'z'.

Reorder the terms:
1 + -323 + -2z + z2 = 323 + -323

Combine like terms: 1 + -323 = -322
-322 + -2z + z2 = 323 + -323

Combine like terms: 323 + -323 = 0
-322 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '322' to each side of the equation.
-322 + -2z + 322 + z2 = 0 + 322

Reorder the terms:
-322 + 322 + -2z + z2 = 0 + 322

Combine like terms: -322 + 322 = 0
0 + -2z + z2 = 0 + 322
-2z + z2 = 0 + 322

Combine like terms: 0 + 322 = 322
-2z + z2 = 322

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = 322 + 1

Reorder the terms:
1 + -2z + z2 = 322 + 1

Combine like terms: 322 + 1 = 323
1 + -2z + z2 = 323

Factor a perfect square on the left side:
(z + -1)(z + -1) = 323

Calculate the square root of the right side: 17.972200756

Break this problem into two subproblems by setting 
(z + -1) equal to 17.972200756 and -17.972200756.

Subproblem 1
z + -1 = 17.972200756

Simplifying
z + -1 = 17.972200756

Reorder the terms:
-1 + z = 17.972200756

Solving
-1 + z = 17.972200756

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z = 17.972200756 + 1

Combine like terms: -1 + 1 = 0
0 + z = 17.972200756 + 1
z = 17.972200756 + 1

Combine like terms: 17.972200756 + 1 = 18.972200756
z = 18.972200756

Simplifying
z = 18.972200756

Subproblem 2
z + -1 = -17.972200756

Simplifying
z + -1 = -17.972200756

Reorder the terms:
-1 + z = -17.972200756

Solving
-1 + z = -17.972200756

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z = -17.972200756 + 1

Combine like terms: -1 + 1 = 0
0 + z = -17.972200756 + 1
z = -17.972200756 + 1

Combine like terms: -17.972200756 + 1 = -16.972200756
z = -16.972200756

Simplifying
z = -16.972200756

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {18.972200756, -16.972200756}