9Y^4-32Y^2-12=0

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Solution for 9Y^4-32Y^2-12=0 equation: 


Simplifying
9Y4 + -32Y2 + -12 = 0

Reorder the terms:
-12 + -32Y2 + 9Y4 = 0

Solving
-12 + -32Y2 + 9Y4 = 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'.
-1.333333333 + -3.555555556Y2 + Y4 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -3.555555556Y2 + 1.333333333 + Y4 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -3.555555556Y2 + Y4 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -3.555555556Y2 + Y4 = 0 + 1.333333333
-3.555555556Y2 + Y4 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-3.555555556Y2 + Y4 = 1.333333333

The Y term is -3.555555556Y2.  Take half its coefficient (-1.777777778).
Square it (3.160493828) and add it to both sides.

Add '3.160493828' to each side of the equation.
-3.555555556Y2 + 3.160493828 + Y4 = 1.333333333 + 3.160493828

Reorder the terms:
3.160493828 + -3.555555556Y2 + Y4 = 1.333333333 + 3.160493828

Combine like terms: 1.333333333 + 3.160493828 = 4.493827161
3.160493828 + -3.555555556Y2 + Y4 = 4.493827161

Factor a perfect square on the left side:
(Y2 + -1.777777778)(Y2 + -1.777777778) = 4.493827161

Calculate the square root of the right side: 2.119864892

Break this problem into two subproblems by setting 
(Y2 + -1.777777778) equal to 2.119864892 and -2.119864892.


Subproblem 1
Y2 + -1.777777778 = 2.119864892

Simplifying
Y2 + -1.777777778 = 2.119864892

Reorder the terms:
-1.777777778 + Y2 = 2.119864892

Solving
-1.777777778 + Y2 = 2.119864892

Solving for variable 'Y'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + Y2 = 2.119864892 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + Y2 = 2.119864892 + 1.777777778
Y2 = 2.119864892 + 1.777777778

Combine like terms: 2.119864892 + 1.777777778 = 3.89764267
Y2 = 3.89764267

Simplifying
Y2 = 3.89764267

Take the square root of each side:
Y = {-1.974244835, 1.974244835}


Subproblem 2
Y2 + -1.777777778 = -2.119864892

Simplifying
Y2 + -1.777777778 = -2.119864892

Reorder the terms:
-1.777777778 + Y2 = -2.119864892

Solving
-1.777777778 + Y2 = -2.119864892

Solving for variable 'Y'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + Y2 = -2.119864892 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + Y2 = -2.119864892 + 1.777777778
Y2 = -2.119864892 + 1.777777778

Combine like terms: -2.119864892 + 1.777777778 = -0.342087114
Y2 = -0.342087114

Simplifying
Y2 = -0.342087114

Reorder the terms:
0.342087114 + Y2 = -0.342087114 + 0.342087114

Combine like terms: -0.342087114 + 0.342087114 = 0.000000000
0.342087114 + Y2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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