Solve each equation:

a)  x^4 - x^2 - 20 =  0

We can actually factor this one in a straightforward manner thusly

(x^2 - 5) ( x^2 + 4) = 0

This means that

x^2 - 5 = 0     add 5 to both sides             

x^2 = 5   take both roots

x = ±√5

Also

x^2 + 4 = 0

x^2 = -4        take both roots

x = ±√[ -4] 

x = ± 2i

And those are the four solutions.....

b )    2x^4 - 50  =  0        divide through by 2

x^4 - 25 =  0           we can factor this as

(x^2 - 5) (x^2 + 5) = 0

This implies that

x^2 - 5 = 0

x^2 = 5      take both roots

x = ±√5

Also

x^2 + 5 =  0

x^2 = -5      take both roots

x = ±√-5

x = ± i√ 5

And those are the four solutions