y+111=y*y

Solution for y+111=y*y equation:

Simplifying
y + 111 = y * y

Reorder the terms:
111 + y = y * y

Multiply y * y
111 + y = y2

Solving
111 + y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
111 + y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-111 + -1y + y2 = 0

Move the constant term to the right:

Add '111' to each side of the equation.
-111 + -1y + 111 + y2 = 0 + 111

Reorder the terms:
-111 + 111 + -1y + y2 = 0 + 111

Combine like terms: -111 + 111 = 0
0 + -1y + y2 = 0 + 111
-1y + y2 = 0 + 111

Combine like terms: 0 + 111 = 111
-1y + y2 = 111

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 111 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 111 + 0.25

Combine like terms: 111 + 0.25 = 111.25
0.25 + -1y + y2 = 111.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 111.25

Calculate the square root of the right side: 10.547511555

Break this problem into two subproblems by setting 
(y + 0.5) equal to 10.547511555 and -10.547511555.

Subproblem 1
y + 0.5 = 10.547511555

Simplifying
y + 0.5 = 10.547511555

Reorder the terms:
0.5 + y = 10.547511555

Solving
0.5 + y = 10.547511555

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 10.547511555 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 10.547511555 + -0.5
y = 10.547511555 + -0.5

Combine like terms: 10.547511555 + -0.5 = 10.047511555
y = 10.047511555

Simplifying
y = 10.047511555

Subproblem 2
y + 0.5 = -10.547511555

Simplifying
y + 0.5 = -10.547511555

Reorder the terms:
0.5 + y = -10.547511555

Solving
0.5 + y = -10.547511555

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -10.547511555 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -10.547511555 + -0.5
y = -10.547511555 + -0.5

Combine like terms: -10.547511555 + -0.5 = -11.047511555
y = -11.047511555

Simplifying
y = -11.047511555

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.047511555, -11.047511555}