3y^4+y^2-1=0

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Solution for 3y^4+y^2-1=0 equation: 


Simplifying
3y4 + y2 + -1 = 0

Reorder the terms:
-1 + y2 + 3y4 = 0

Solving
-1 + y2 + 3y4 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-0.3333333333 + 0.3333333333y2 + y4 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.3333333333y2 + 0.3333333333 + y4 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.3333333333y2 + y4 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.3333333333y2 + y4 = 0 + 0.3333333333
0.3333333333y2 + y4 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.3333333333y2 + y4 = 0.3333333333

The y term is y2.  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.
0.3333333333y2 + 0.25 + y4 = 0.3333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333y2 + y4 = 0.3333333333 + 0.25

Combine like terms: 0.3333333333 + 0.25 = 0.5833333333
0.25 + 0.3333333333y2 + y4 = 0.5833333333

Factor a perfect square on the left side:
(y2 + 0.5)(y2 + 0.5) = 0.5833333333

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(y2 + 0.5) equal to 0.763762616 and -0.763762616.


Subproblem 1
y2 + 0.5 = 0.763762616

Simplifying
y2 + 0.5 = 0.763762616

Reorder the terms:
0.5 + y2 = 0.763762616

Solving
0.5 + y2 = 0.763762616

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 + y2 = 0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y2 = 0.763762616 + -0.5
y2 = 0.763762616 + -0.5

Combine like terms: 0.763762616 + -0.5 = 0.263762616
y2 = 0.263762616

Simplifying
y2 = 0.263762616

Take the square root of each side:
y = {-0.513578247, 0.513578247}


Subproblem 2
y2 + 0.5 = -0.763762616

Simplifying
y2 + 0.5 = -0.763762616

Reorder the terms:
0.5 + y2 = -0.763762616

Solving
0.5 + y2 = -0.763762616

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 + y2 = -0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y2 = -0.763762616 + -0.5
y2 = -0.763762616 + -0.5

Combine like terms: -0.763762616 + -0.5 = -1.263762616
y2 = -1.263762616

Simplifying
y2 = -1.263762616

Reorder the terms:
1.263762616 + y2 = -1.263762616 + 1.263762616

Combine like terms: -1.263762616 + 1.263762616 = 0.000000000
1.263762616 + 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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