y^2+33=12y

Solution for y^2+33=12y equation:

Simplifying
y2 + 33 = 12y

Reorder the terms:
33 + y2 = 12y

Solving
33 + y2 = 12y

Solving for variable 'y'.

Reorder the terms:
33 + -12y + y2 = 12y + -12y

Combine like terms: 12y + -12y = 0
33 + -12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + -12y + -33 + y2 = 0 + -33

Reorder the terms:
33 + -33 + -12y + y2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -12y + y2 = 0 + -33
-12y + y2 = 0 + -33

Combine like terms: 0 + -33 = -33
-12y + y2 = -33

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = -33 + 36

Reorder the terms:
36 + -12y + y2 = -33 + 36

Combine like terms: -33 + 36 = 3
36 + -12y + y2 = 3

Factor a perfect square on the left side:
(y + -6)(y + -6) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + -6) equal to 1.732050808 and -1.732050808.

Subproblem 1
y + -6 = 1.732050808

Simplifying
y + -6 = 1.732050808

Reorder the terms:
-6 + y = 1.732050808

Solving
-6 + y = 1.732050808

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = 1.732050808 + 6

Combine like terms: -6 + 6 = 0
0 + y = 1.732050808 + 6
y = 1.732050808 + 6

Combine like terms: 1.732050808 + 6 = 7.732050808
y = 7.732050808

Simplifying
y = 7.732050808

Subproblem 2
y + -6 = -1.732050808

Simplifying
y + -6 = -1.732050808

Reorder the terms:
-6 + y = -1.732050808

Solving
-6 + y = -1.732050808

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = -1.732050808 + 6

Combine like terms: -6 + 6 = 0
0 + y = -1.732050808 + 6
y = -1.732050808 + 6

Combine like terms: -1.732050808 + 6 = 4.267949192
y = 4.267949192

Simplifying
y = 4.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.732050808, 4.267949192}