2s^4+s^2-1=0

Solution for 2s^4+s^2-1=0 equation:

Simplifying
2s4 + s2 + -1 = 0

Reorder the terms:
-1 + s2 + 2s4 = 0

Solving
-1 + s2 + 2s4 = 0

Solving for variable 's'.

Factor a trinomial.
(-1 + -1s2)(1 + -2s2) = 0

Subproblem 1
Set the factor '(-1 + -1s2)' equal to zero and attempt to solve:

Simplifying
-1 + -1s2 = 0

Solving
-1 + -1s2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1s2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1s2 = 0 + 1
-1s2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1s2 = 1

Divide each side by '-1'.
s2 = -1

Simplifying
s2 = -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 '(1 + -2s2)' equal to zero and attempt to solve:

Simplifying
1 + -2s2 = 0

Solving
1 + -2s2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2s2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2s2 = 0 + -1
-2s2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2s2 = -1

Divide each side by '-2'.
s2 = 0.5

Simplifying
s2 = 0.5

Take the square root of each side:
s = {-0.707106781, 0.707106781}
Solution
s = {-0.707106781, 0.707106781}