9x^8-37x^4y^4+4y^8=0

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Solution for 9x^8-37x^4y^4+4y^8=0 equation: 


Simplifying
9x8 + -37x4y4 + 4y8 = 0

Reorder the terms:
-37x4y4 + 9x8 + 4y8 = 0

Solving
-37x4y4 + 9x8 + 4y8 = 0

Solving for variable 'x'.

Factor a trinomial.
(x4 + -4y4)(9x4 + -1y4) = 0

Factor a difference between two squares.
((x2 + 2y2)(x2 + -2y2))(9x4 + -1y4) = 0

Factor a difference between two squares.
((3x2 + y2)(3x2 + -1y2))(x2 + 2y2)(x2 + -2y2) = 0


Subproblem 1
Set the factor '(x2 + 2y2)' equal to zero and attempt to solve:

Simplifying
x2 + 2y2 = 0

Solving
x2 + 2y2 = 0

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

Add '-2y2' to each side of the equation.
x2 + 2y2 + -2y2 = 0 + -2y2

Combine like terms: 2y2 + -2y2 = 0
x2 + 0 = 0 + -2y2
x2 = 0 + -2y2
Remove the zero:
x2 = -2y2

Simplifying
x2 = -2y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(x2 + -2y2)' equal to zero and attempt to solve:

Simplifying
x2 + -2y2 = 0

Solving
x2 + -2y2 = 0

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

Add '2y2' to each side of the equation.
x2 + -2y2 + 2y2 = 0 + 2y2

Combine like terms: -2y2 + 2y2 = 0
x2 + 0 = 0 + 2y2
x2 = 0 + 2y2
Remove the zero:
x2 = 2y2

Simplifying
x2 = 2y2

Take the square root of each side:
x = {-1.414213562y, 1.414213562y}

Subproblem 3
Set the factor '(3x2 + y2)' equal to zero and attempt to solve:

Simplifying
3x2 + y2 = 0

Solving
3x2 + y2 = 0

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

Add '-1y2' to each side of the equation.
3x2 + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
3x2 + 0 = 0 + -1y2
3x2 = 0 + -1y2
Remove the zero:
3x2 = -1y2

Divide each side by '3'.
x2 = -0.3333333333y2

Simplifying
x2 = -0.3333333333y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 4
Set the factor '(3x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
3x2 + -1y2 = 0

Solving
3x2 + -1y2 = 0

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

Add 'y2' to each side of the equation.
3x2 + -1y2 + y2 = 0 + y2

Combine like terms: -1y2 + y2 = 0
3x2 + 0 = 0 + y2
3x2 = 0 + y2
Remove the zero:
3x2 = y2

Divide each side by '3'.
x2 = 0.3333333333y2

Simplifying
x2 = 0.3333333333y2

Take the square root of each side:
x = {-0.577350269y, 0.577350269y}
Solution
x = {-1.414213562y, 1.414213562y, -0.577350269y, 0.577350269y}

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