5z^2-2z+1=0

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

Simplifying
5z2 + -2z + 1 = 0

Reorder the terms:
1 + -2z + 5z2 = 0

Solving
1 + -2z + 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 + -0.4z + z2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.4z + -0.2 + z2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.4z + z2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.4z + z2 = 0 + -0.2
-0.4z + z2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.4z + z2 = -0.2

The z term is -0.4z.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4z + 0.04 + z2 = -0.2 + 0.04

Reorder the terms:
0.04 + -0.4z + z2 = -0.2 + 0.04

Combine like terms: -0.2 + 0.04 = -0.16
0.04 + -0.4z + z2 = -0.16

Factor a perfect square on the left side:
(z + -0.2)(z + -0.2) = -0.16

Can't calculate square root of the right side.

The solution to this equation could not be determined.