x^4+x^2y^2-25y^4=0

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Solution for x^4+x^2y^2-25y^4=0 equation: 


Simplifying
x4 + x2y2 + -25y4 = 0

Reorder the terms:
x2y2 + x4 + -25y4 = 0

Solving
x2y2 + x4 + -25y4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '25y4' to each side of the equation.
x2y2 + x4 + -25y4 + 25y4 = 0 + 25y4

Combine like terms: -25y4 + 25y4 = 0
x2y2 + x4 + 0 = 0 + 25y4
x2y2 + x4 = 0 + 25y4
Remove the zero:
x2y2 + x4 = 25y4

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 = 25y4 + 0.25y4

Combine like terms: 25y4 + 0.25y4 = 25.25y4
x2y2 + x4 + 0.25y4 = 25.25y4

Factor a perfect square on the left side:
(x2 + 0.5y2)(x2 + 0.5y2) = 25.25y4

Calculate the square root of the right side: 5.024937811y2

Break this problem into two subproblems by setting 
(x2 + 0.5y2) equal to 5.024937811y2 and -5.024937811y2.


Subproblem 1
x2 + 0.5y2 = 5.024937811y2

Simplifying
x2 + 0.5y2 = 5.024937811y2

Solving
x2 + 0.5y2 = 5.024937811y2

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 = 5.024937811y2 + -0.5y2

Combine like terms: 0.5y2 + -0.5y2 = 0.0
x2 + 0.0 = 5.024937811y2 + -0.5y2
x2 = 5.024937811y2 + -0.5y2

Combine like terms: 5.024937811y2 + -0.5y2 = 4.524937811y2
x2 = 4.524937811y2

Simplifying
x2 = 4.524937811y2

Take the square root of each side:
x = {-2.127190121y, 2.127190121y}


Subproblem 2
x2 + 0.5y2 = -5.024937811y

Simplifying
x2 + 0.5y2 = -5.024937811y

Solving
x2 + 0.5y2 = -5.024937811y

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 = -5.024937811y + -0.5y2

Combine like terms: 0.5y2 + -0.5y2 = 0.0
x2 + 0.0 = -5.024937811y + -0.5y2
x2 = -5.024937811y + -0.5y2

Simplifying
x2 = -5.024937811y + -0.5y2

Reorder the terms:
x2 + 5.024937811y + 0.5y2 = -5.024937811y + 5.024937811y + -0.5y2 + 0.5y2

Combine like terms: -5.024937811y + 5.024937811y = 0.000000000
x2 + 5.024937811y + 0.5y2 = 0.000000000 + -0.5y2 + 0.5y2
x2 + 5.024937811y + 0.5y2 = -0.5y2 + 0.5y2

Combine like terms: -0.5y2 + 0.5y2 = 0.0
x2 + 5.024937811y + 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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