-y^2+9y-9=0

Solution for -y^2+9y-9=0 equation:

Simplifying
-1y2 + 9y + -9 = 0

Reorder the terms:
-9 + 9y + -1y2 = 0

Solving
-9 + 9y + -1y2 = 0

Solving for variable 'y'.

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

Divide each side by '-1'.
9 + -9y + y2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -9y + -9 + y2 = 0 + -9

Reorder the terms:
9 + -9 + -9y + y2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -9y + y2 = 0 + -9
-9y + y2 = 0 + -9

Combine like terms: 0 + -9 = -9
-9y + y2 = -9

The y term is -9y.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9y + 20.25 + y2 = -9 + 20.25

Reorder the terms:
20.25 + -9y + y2 = -9 + 20.25

Combine like terms: -9 + 20.25 = 11.25
20.25 + -9y + y2 = 11.25

Factor a perfect square on the left side:
(y + -4.5)(y + -4.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(y + -4.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
y + -4.5 = 3.354101966

Simplifying
y + -4.5 = 3.354101966

Reorder the terms:
-4.5 + y = 3.354101966

Solving
-4.5 + y = 3.354101966

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = 3.354101966 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = 3.354101966 + 4.5
y = 3.354101966 + 4.5

Combine like terms: 3.354101966 + 4.5 = 7.854101966
y = 7.854101966

Simplifying
y = 7.854101966

Subproblem 2
y + -4.5 = -3.354101966

Simplifying
y + -4.5 = -3.354101966

Reorder the terms:
-4.5 + y = -3.354101966

Solving
-4.5 + y = -3.354101966

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = -3.354101966 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = -3.354101966 + 4.5
y = -3.354101966 + 4.5

Combine like terms: -3.354101966 + 4.5 = 1.145898034
y = 1.145898034

Simplifying
y = 1.145898034

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.854101966, 1.145898034}