2y^2-5y+1=0

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

Simplifying
2y2 + -5y + 1 = 0

Reorder the terms:
1 + -5y + 2y2 = 0

Solving
1 + -5y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
0.5 + -2.5y + y2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2.5y + -0.5 + y2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2.5y + y2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2.5y + y2 = 0 + -0.5
-2.5y + y2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-2.5y + y2 = -0.5

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = -0.5 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = -0.5 + 1.5625

Combine like terms: -0.5 + 1.5625 = 1.0625
1.5625 + -2.5y + y2 = 1.0625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(y + -1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
y + -1.25 = 1.030776406

Simplifying
y + -1.25 = 1.030776406

Reorder the terms:
-1.25 + y = 1.030776406

Solving
-1.25 + y = 1.030776406

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 1.030776406 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 1.030776406 + 1.25
y = 1.030776406 + 1.25

Combine like terms: 1.030776406 + 1.25 = 2.280776406
y = 2.280776406

Simplifying
y = 2.280776406

Subproblem 2
y + -1.25 = -1.030776406

Simplifying
y + -1.25 = -1.030776406

Reorder the terms:
-1.25 + y = -1.030776406

Solving
-1.25 + y = -1.030776406

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -1.030776406 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -1.030776406 + 1.25
y = -1.030776406 + 1.25

Combine like terms: -1.030776406 + 1.25 = 0.219223594
y = 0.219223594

Simplifying
y = 0.219223594

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.280776406, 0.219223594}