a^4-7a^2-8=0

Solution for a^4-7a^2-8=0 equation:

Simplifying
a4 + -7a2 + -8 = 0

Reorder the terms:
-8 + -7a2 + a4 = 0

Solving
-8 + -7a2 + a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -1a2)(8 + -1a2) = 0

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

Simplifying
-1 + -1a2 = 0

Solving
-1 + -1a2 = 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 + -1a2 = 0 + 1

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

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

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

Simplifying
a2 = -1

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 '(8 + -1a2)' equal to zero and attempt to solve:

Simplifying
8 + -1a2 = 0

Solving
8 + -1a2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a2 = 0 + -8
-1a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1a2 = -8

Divide each side by '-1'.
a2 = 8

Simplifying
a2 = 8

Take the square root of each side:
a = {-2.828427125, 2.828427125}
Solution
a = {-2.828427125, 2.828427125}