16y^4-y^2-12=0

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Solution for 16y^4-y^2-12=0 equation: 


Simplifying
16y4 + -1y2 + -12 = 0

Reorder the terms:
-12 + -1y2 + 16y4 = 0

Solving
-12 + -1y2 + 16y4 = 0

Solving for variable 'y'.

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

Divide each side by '16'.
-0.75 + -0.0625y2 + y4 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.0625y2 + 0.75 + y4 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.0625y2 + y4 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.0625y2 + y4 = 0 + 0.75
-0.0625y2 + y4 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.0625y2 + y4 = 0.75

The y term is -0.0625y2.  Take half its coefficient (-0.03125).
Square it (0.0009765625) and add it to both sides.

Add '0.0009765625' to each side of the equation.
-0.0625y2 + 0.0009765625 + y4 = 0.75 + 0.0009765625

Reorder the terms:
0.0009765625 + -0.0625y2 + y4 = 0.75 + 0.0009765625

Combine like terms: 0.75 + 0.0009765625 = 0.7509765625
0.0009765625 + -0.0625y2 + y4 = 0.7509765625

Factor a perfect square on the left side:
(y2 + -0.03125)(y2 + -0.03125) = 0.7509765625

Calculate the square root of the right side: 0.866589039

Break this problem into two subproblems by setting 
(y2 + -0.03125) equal to 0.866589039 and -0.866589039.


Subproblem 1
y2 + -0.03125 = 0.866589039

Simplifying
y2 + -0.03125 = 0.866589039

Reorder the terms:
-0.03125 + y2 = 0.866589039

Solving
-0.03125 + y2 = 0.866589039

Solving for variable 'y'.

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

Add '0.03125' to each side of the equation.
-0.03125 + 0.03125 + y2 = 0.866589039 + 0.03125

Combine like terms: -0.03125 + 0.03125 = 0.00000
0.00000 + y2 = 0.866589039 + 0.03125
y2 = 0.866589039 + 0.03125

Combine like terms: 0.866589039 + 0.03125 = 0.897839039
y2 = 0.897839039

Simplifying
y2 = 0.897839039

Take the square root of each side:
y = {-0.947543687, 0.947543687}


Subproblem 2
y2 + -0.03125 = -0.866589039

Simplifying
y2 + -0.03125 = -0.866589039

Reorder the terms:
-0.03125 + y2 = -0.866589039

Solving
-0.03125 + y2 = -0.866589039

Solving for variable 'y'.

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

Add '0.03125' to each side of the equation.
-0.03125 + 0.03125 + y2 = -0.866589039 + 0.03125

Combine like terms: -0.03125 + 0.03125 = 0.00000
0.00000 + y2 = -0.866589039 + 0.03125
y2 = -0.866589039 + 0.03125

Combine like terms: -0.866589039 + 0.03125 = -0.835339039
y2 = -0.835339039

Simplifying
y2 = -0.835339039

Reorder the terms:
0.835339039 + y2 = -0.835339039 + 0.835339039

Combine like terms: -0.835339039 + 0.835339039 = 0.000000000
0.835339039 + 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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