4z^2-20z+41=0

Solution for 4z^2-20z+41=0 equation:

Simplifying
4z2 + -20z + 41 = 0

Reorder the terms:
41 + -20z + 4z2 = 0

Solving
41 + -20z + 4z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
10.25 + -5z + z2 = 0

Move the constant term to the right:

Add '-10.25' to each side of the equation.
10.25 + -5z + -10.25 + z2 = 0 + -10.25

Reorder the terms:
10.25 + -10.25 + -5z + z2 = 0 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + -5z + z2 = 0 + -10.25
-5z + z2 = 0 + -10.25

Combine like terms: 0 + -10.25 = -10.25
-5z + z2 = -10.25

The z term is -5z.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5z + 6.25 + z2 = -10.25 + 6.25

Reorder the terms:
6.25 + -5z + z2 = -10.25 + 6.25

Combine like terms: -10.25 + 6.25 = -4
6.25 + -5z + z2 = -4

Factor a perfect square on the left side:
(z + -2.5)(z + -2.5) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.