y^2-6y+6=0

Solution for y^2-6y+6=0 equation:

Simplifying
y2 + -6y + 6 = 0

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

Solving
6 + -6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -6 + 9

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

Combine like terms: -6 + 9 = 3
9 + -6y + y2 = 3

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

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + -3) equal to 1.732050808 and -1.732050808.

Subproblem 1
y + -3 = 1.732050808

Simplifying
y + -3 = 1.732050808

Reorder the terms:
-3 + y = 1.732050808

Solving
-3 + y = 1.732050808

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 = 1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + y = 1.732050808 + 3
y = 1.732050808 + 3

Combine like terms: 1.732050808 + 3 = 4.732050808
y = 4.732050808

Simplifying
y = 4.732050808

Subproblem 2
y + -3 = -1.732050808

Simplifying
y + -3 = -1.732050808

Reorder the terms:
-3 + y = -1.732050808

Solving
-3 + y = -1.732050808

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 = -1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + y = -1.732050808 + 3
y = -1.732050808 + 3

Combine like terms: -1.732050808 + 3 = 1.267949192
y = 1.267949192

Simplifying
y = 1.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.732050808, 1.267949192}