2y^2-12y+11=0

Solution for 2y^2-12y+11=0 equation:

Simplifying
2y2 + -12y + 11 = 0

Reorder the terms:
11 + -12y + 2y2 = 0

Solving
11 + -12y + 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'.
5.5 + -6y + y2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -6y + -5.5 + y2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -6y + y2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -6y + y2 = 0 + -5.5
-6y + y2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-6y + y2 = -5.5

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = -5.5 + 9

Reorder the terms:
9 + -6y + y2 = -5.5 + 9

Combine like terms: -5.5 + 9 = 3.5
9 + -6y + y2 = 3.5

Factor a perfect square on the left side:
(y + -3)(y + -3) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(y + -3) equal to 1.870828693 and -1.870828693.

Subproblem 1
y + -3 = 1.870828693

Simplifying
y + -3 = 1.870828693

Reorder the terms:
-3 + y = 1.870828693

Solving
-3 + y = 1.870828693

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = 1.870828693 + 3

Combine like terms: -3 + 3 = 0
0 + y = 1.870828693 + 3
y = 1.870828693 + 3

Combine like terms: 1.870828693 + 3 = 4.870828693
y = 4.870828693

Simplifying
y = 4.870828693

Subproblem 2
y + -3 = -1.870828693

Simplifying
y + -3 = -1.870828693

Reorder the terms:
-3 + y = -1.870828693

Solving
-3 + y = -1.870828693

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = -1.870828693 + 3

Combine like terms: -3 + 3 = 0
0 + y = -1.870828693 + 3
y = -1.870828693 + 3

Combine like terms: -1.870828693 + 3 = 1.129171307
y = 1.129171307

Simplifying
y = 1.129171307

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.870828693, 1.129171307}