9y^2-66y-11=0

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Solution for 9y^2-66y-11=0 equation: 


Simplifying
9y2 + -66y + -11 = 0

Reorder the terms:
-11 + -66y + 9y2 = 0

Solving
-11 + -66y + 9y2 = 0

Solving for variable 'y'.

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

Divide each side by '9'.
-1.222222222 + -7.333333333y + y2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + -7.333333333y + 1.222222222 + y2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + -7.333333333y + y2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + -7.333333333y + y2 = 0 + 1.222222222
-7.333333333y + y2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
-7.333333333y + y2 = 1.222222222

The y term is -7.333333333y.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333y + 13.44444445 + y2 = 1.222222222 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333y + y2 = 1.222222222 + 13.44444445

Combine like terms: 1.222222222 + 13.44444445 = 14.666666672
13.44444445 + -7.333333333y + y2 = 14.666666672

Factor a perfect square on the left side:
(y + -3.666666667)(y + -3.666666667) = 14.666666672

Calculate the square root of the right side: 3.829708432

Break this problem into two subproblems by setting 
(y + -3.666666667) equal to 3.829708432 and -3.829708432.


Subproblem 1
y + -3.666666667 = 3.829708432

Simplifying
y + -3.666666667 = 3.829708432

Reorder the terms:
-3.666666667 + y = 3.829708432

Solving
-3.666666667 + y = 3.829708432

Solving for variable 'y'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + y = 3.829708432 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + y = 3.829708432 + 3.666666667
y = 3.829708432 + 3.666666667

Combine like terms: 3.829708432 + 3.666666667 = 7.496375099
y = 7.496375099

Simplifying
y = 7.496375099


Subproblem 2
y + -3.666666667 = -3.829708432

Simplifying
y + -3.666666667 = -3.829708432

Reorder the terms:
-3.666666667 + y = -3.829708432

Solving
-3.666666667 + y = -3.829708432

Solving for variable 'y'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + y = -3.829708432 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + y = -3.829708432 + 3.666666667
y = -3.829708432 + 3.666666667

Combine like terms: -3.829708432 + 3.666666667 = -0.163041765
y = -0.163041765

Simplifying
y = -0.163041765


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.496375099, -0.163041765}

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