5z^2-4z+1=0

Solution for 5z^2-4z+1=0 equation:

Simplifying
5z2 + -4z + 1 = 0

Reorder the terms:
1 + -4z + 5z2 = 0

Solving
1 + -4z + 5z2 = 0

Solving for variable 'z'.

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

Divide each side by '5'.
0.2 + -0.8z + z2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.8z + -0.2 + z2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.8z + z2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.8z + z2 = 0 + -0.2
-0.8z + z2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.8z + z2 = -0.2

The z term is -0.8z.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8z + 0.16 + z2 = -0.2 + 0.16

Reorder the terms:
0.16 + -0.8z + z2 = -0.2 + 0.16

Combine like terms: -0.2 + 0.16 = -0.04
0.16 + -0.8z + z2 = -0.04

Factor a perfect square on the left side:
(z + -0.4)(z + -0.4) = -0.04

Can't calculate square root of the right side.

The solution to this equation could not be determined.