7z^2-2z+1=0

Solution for 7z^2-2z+1=0 equation:

Simplifying
7z2 + -2z + 1 = 0

Reorder the terms:
1 + -2z + 7z2 = 0

Solving
1 + -2z + 7z2 = 0

Solving for variable 'z'.

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

Divide each side by '7'.
0.1428571429 + -0.2857142857z + z2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.2857142857z + -0.1428571429 + z2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -0.2857142857z + z2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -0.2857142857z + z2 = 0 + -0.1428571429
-0.2857142857z + z2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-0.2857142857z + z2 = -0.1428571429

The z term is -0.2857142857z.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857z + 0.02040816328 + z2 = -0.1428571429 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857z + z2 = -0.1428571429 + 0.02040816328

Combine like terms: -0.1428571429 + 0.02040816328 = -0.12244897962
0.02040816328 + -0.2857142857z + z2 = -0.12244897962

Factor a perfect square on the left side:
(z + -0.1428571429)(z + -0.1428571429) = -0.12244897962

Can't calculate square root of the right side.

The solution to this equation could not be determined.