z^2-4z+5=0

Solution for z^2-4z+5=0 equation:

Simplifying
z2 + -4z + 5 = 0

Reorder the terms:
5 + -4z + z2 = 0

Solving
5 + -4z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -4z + -5 + z2 = 0 + -5

Reorder the terms:
5 + -5 + -4z + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z + z2 = 0 + -5
-4z + z2 = 0 + -5

Combine like terms: 0 + -5 = -5
-4z + z2 = -5

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = -5 + 4

Reorder the terms:
4 + -4z + z2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + -4z + z2 = -1

Factor a perfect square on the left side:
(z + -2)(z + -2) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.