2a^4-a^2-1=0

Solution for 2a^4-a^2-1=0 equation:

Simplifying
2a4 + -1a2 + -1 = 0

Reorder the terms:
-1 + -1a2 + 2a4 = 0

Solving
-1 + -1a2 + 2a4 = 0

Solving for variable 'a'.

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

Factor a difference between two squares.
(-1 + -2a2)((1 + a)(1 + -1a)) = 0

Subproblem 1
Set the factor '(-1 + -2a2)' equal to zero and attempt to solve:

Simplifying
-1 + -2a2 = 0

Solving
-1 + -2a2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a2 = 0 + 1
-2a2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2a2 = 1

Divide each side by '-2'.
a2 = -0.5

Simplifying
a2 = -0.5

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 '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Subproblem 3
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {-1, 1}