9y^2-12y-2=0

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Solution for 9y^2-12y-2=0 equation: 


Simplifying
9y2 + -12y + -2 = 0

Reorder the terms:
-2 + -12y + 9y2 = 0

Solving
-2 + -12y + 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'.
-0.2222222222 + -1.333333333y + y2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -1.333333333y + 0.2222222222 + y2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -1.333333333y + y2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -1.333333333y + y2 = 0 + 0.2222222222
-1.333333333y + y2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-1.333333333y + y2 = 0.2222222222

The y term is -1.333333333y.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333y + 0.4444444442 + y2 = 0.2222222222 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333y + y2 = 0.2222222222 + 0.4444444442

Combine like terms: 0.2222222222 + 0.4444444442 = 0.6666666664
0.4444444442 + -1.333333333y + y2 = 0.6666666664

Factor a perfect square on the left side:
(y + -0.6666666665)(y + -0.6666666665) = 0.6666666664

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(y + -0.6666666665) equal to 0.816496581 and -0.816496581.


Subproblem 1
y + -0.6666666665 = 0.816496581

Simplifying
y + -0.6666666665 = 0.816496581

Reorder the terms:
-0.6666666665 + y = 0.816496581

Solving
-0.6666666665 + y = 0.816496581

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = 0.816496581 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = 0.816496581 + 0.6666666665
y = 0.816496581 + 0.6666666665

Combine like terms: 0.816496581 + 0.6666666665 = 1.4831632475
y = 1.4831632475

Simplifying
y = 1.4831632475


Subproblem 2
y + -0.6666666665 = -0.816496581

Simplifying
y + -0.6666666665 = -0.816496581

Reorder the terms:
-0.6666666665 + y = -0.816496581

Solving
-0.6666666665 + y = -0.816496581

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = -0.816496581 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = -0.816496581 + 0.6666666665
y = -0.816496581 + 0.6666666665

Combine like terms: -0.816496581 + 0.6666666665 = -0.1498299145
y = -0.1498299145

Simplifying
y = -0.1498299145


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.4831632475, -0.1498299145}

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