x^4+y^2*x^2-y^4=0

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Solution for x^4+y^2*x^2-y^4=0 equation: 


Simplifying
x4 + y2 * x2 + -1y4 = 0

Multiply y2 * x2
x4 + x2y2 + -1y4 = 0

Reorder the terms:
x2y2 + x4 + -1y4 = 0

Solving
x2y2 + x4 + -1y4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add 'y4' to each side of the equation.
x2y2 + x4 + -1y4 + y4 = 0 + y4

Combine like terms: -1y4 + y4 = 0
x2y2 + x4 + 0 = 0 + y4
x2y2 + x4 = 0 + y4
Remove the zero:
x2y2 + x4 = y4

The x term is x2y2.  Take half its coefficient (0.5y2).
Square it (0.25y4) and add it to both sides.

Add '0.25y4' to each side of the equation.
x2y2 + x4 + 0.25y4 = y4 + 0.25y4

Combine like terms: y4 + 0.25y4 = 1.25y4
x2y2 + x4 + 0.25y4 = 1.25y4

Factor a perfect square on the left side:
(x2 + 0.5y2)(x2 + 0.5y2) = 1.25y4

Calculate the square root of the right side: 1.118033989y2

Break this problem into two subproblems by setting 
(x2 + 0.5y2) equal to 1.118033989y2 and -1.118033989y2.


Subproblem 1
x2 + 0.5y2 = 1.118033989y2

Simplifying
x2 + 0.5y2 = 1.118033989y2

Solving
x2 + 0.5y2 = 1.118033989y2

Solving for variable 'x'.

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

Add '-0.5y2' to each side of the equation.
x2 + 0.5y2 + -0.5y2 = 1.118033989y2 + -0.5y2

Combine like terms: 0.5y2 + -0.5y2 = 0.0
x2 + 0.0 = 1.118033989y2 + -0.5y2
x2 = 1.118033989y2 + -0.5y2

Combine like terms: 1.118033989y2 + -0.5y2 = 0.618033989y2
x2 = 0.618033989y2

Simplifying
x2 = 0.618033989y2

Take the square root of each side:
x = {-0.786151378y, 0.786151378y}


Subproblem 2
x2 + 0.5y2 = -1.118033989y

Simplifying
x2 + 0.5y2 = -1.118033989y

Solving
x2 + 0.5y2 = -1.118033989y

Solving for variable 'x'.

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

Add '-0.5y2' to each side of the equation.
x2 + 0.5y2 + -0.5y2 = -1.118033989y + -0.5y2

Combine like terms: 0.5y2 + -0.5y2 = 0.0
x2 + 0.0 = -1.118033989y + -0.5y2
x2 = -1.118033989y + -0.5y2

Simplifying
x2 = -1.118033989y + -0.5y2

Reorder the terms:
x2 + 1.118033989y + 0.5y2 = -1.118033989y + 1.118033989y + -0.5y2 + 0.5y2

Combine like terms: -1.118033989y + 1.118033989y = 0.000000000
x2 + 1.118033989y + 0.5y2 = 0.000000000 + -0.5y2 + 0.5y2
x2 + 1.118033989y + 0.5y2 = -0.5y2 + 0.5y2

Combine like terms: -0.5y2 + 0.5y2 = 0.0
x2 + 1.118033989y + 0.5y2 = 0.0

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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