a^4+a^2*b^2-b^4=0

Solution for a^4+a^2*b^2-b^4=0 equation:

Simplifying
a4 + a2 * b2 + -1b4 = 0

Multiply a2 * b2
a4 + a2b2 + -1b4 = 0

Reorder the terms:
a2b2 + a4 + -1b4 = 0

Solving
a2b2 + a4 + -1b4 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add 'b4' to each side of the equation.
a2b2 + a4 + -1b4 + b4 = 0 + b4

Combine like terms: -1b4 + b4 = 0
a2b2 + a4 + 0 = 0 + b4
a2b2 + a4 = 0 + b4
Remove the zero:
a2b2 + a4 = b4

The a term is a2b2.  Take half its coefficient (0.5b2).
Square it (0.25b4) and add it to both sides.

Add '0.25b4' to each side of the equation.
a2b2 + a4 + 0.25b4 = b4 + 0.25b4

Combine like terms: b4 + 0.25b4 = 1.25b4
a2b2 + a4 + 0.25b4 = 1.25b4

Factor a perfect square on the left side:
(a2 + 0.5b2)(a2 + 0.5b2) = 1.25b4

Calculate the square root of the right side: 1.118033989b2

Break this problem into two subproblems by setting 
(a2 + 0.5b2) equal to 1.118033989b2 and -1.118033989b2.

Subproblem 1
a2 + 0.5b2 = 1.118033989b2

Simplifying
a2 + 0.5b2 = 1.118033989b2

Solving
a2 + 0.5b2 = 1.118033989b2

Solving for variable 'a'.

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

Add '-0.5b2' to each side of the equation.
a2 + 0.5b2 + -0.5b2 = 1.118033989b2 + -0.5b2

Combine like terms: 0.5b2 + -0.5b2 = 0.0
a2 + 0.0 = 1.118033989b2 + -0.5b2
a2 = 1.118033989b2 + -0.5b2

Combine like terms: 1.118033989b2 + -0.5b2 = 0.618033989b2
a2 = 0.618033989b2

Simplifying
a2 = 0.618033989b2

Take the square root of each side:
a = {-0.786151378b, 0.786151378b}

Subproblem 2
a2 + 0.5b2 = -1.118033989b

Simplifying
a2 + 0.5b2 = -1.118033989b

Solving
a2 + 0.5b2 = -1.118033989b

Solving for variable 'a'.

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

Add '-0.5b2' to each side of the equation.
a2 + 0.5b2 + -0.5b2 = -1.118033989b + -0.5b2

Combine like terms: 0.5b2 + -0.5b2 = 0.0
a2 + 0.0 = -1.118033989b + -0.5b2
a2 = -1.118033989b + -0.5b2

Simplifying
a2 = -1.118033989b + -0.5b2

Reorder the terms:
a2 + 1.118033989b + 0.5b2 = -1.118033989b + 1.118033989b + -0.5b2 + 0.5b2

Combine like terms: -1.118033989b + 1.118033989b = 0.000000000
a2 + 1.118033989b + 0.5b2 = 0.000000000 + -0.5b2 + 0.5b2
a2 + 1.118033989b + 0.5b2 = -0.5b2 + 0.5b2

Combine like terms: -0.5b2 + 0.5b2 = 0.0
a2 + 1.118033989b + 0.5b2 = 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.