z^2-4z+13=0

Solution for z^2-4z+13=0 equation:

Simplifying
z2 + -4z + 13 = 0

Reorder the terms:
13 + -4z + z2 = 0

Solving
13 + -4z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -4z + -13 + z2 = 0 + -13

Reorder the terms:
13 + -13 + -4z + z2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4z + z2 = 0 + -13
-4z + z2 = 0 + -13

Combine like terms: 0 + -13 = -13
-4z + z2 = -13

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 = -13 + 4

Reorder the terms:
4 + -4z + z2 = -13 + 4

Combine like terms: -13 + 4 = -9
4 + -4z + z2 = -9

Factor a perfect square on the left side:
(z + -2)(z + -2) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.