2x^4+a^2x^2-a^4=0

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

Simplifying
2x4 + a2x2 + -1a4 = 0

Reorder the terms:
a2x2 + -1a4 + 2x4 = 0

Solving
a2x2 + -1a4 + 2x4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1a2 + -1x2)(a2 + -2x2) = 0

Subproblem 1
Set the factor '(-1a2 + -1x2)' equal to zero and attempt to solve:

Simplifying
-1a2 + -1x2 = 0

Solving
-1a2 + -1x2 = 0

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

Add 'x2' to each side of the equation.
-1a2 + -1x2 + x2 = 0 + x2

Combine like terms: -1x2 + x2 = 0
-1a2 + 0 = 0 + x2
-1a2 = 0 + x2
Remove the zero:
-1a2 = x2

Divide each side by '-1'.
a2 = -1x2

Simplifying
a2 = -1x2

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 '(a2 + -2x2)' equal to zero and attempt to solve:

Simplifying
a2 + -2x2 = 0

Solving
a2 + -2x2 = 0

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

Add '2x2' to each side of the equation.
a2 + -2x2 + 2x2 = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
a2 + 0 = 0 + 2x2
a2 = 0 + 2x2
Remove the zero:
a2 = 2x2

Simplifying
a2 = 2x2

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