algebra

If you had the problem       :  x² - 21x - 100  =  0

you would factor it this way:  (x - 25)(x + 4)  =  0

and the solutions are:  25,  -4

 

Since you have:     x⁴ - 21x² - 100  =  0

factor it as:           (x² - 25)(x² + 4)  =  0

 

This can be further factored as:                                            (x - 5)(x + 5)(x² + 4)  =  0

If you have complex numbers you can factor again:   (x - 5)(x + 5)(x - 2i)(x + 2i)  =  0

and the solutions are:  5,  -5,  2i,  -2i

 

If you don't have complex numbers, stop with:  (x - 5)(x + 5)(x² + 4)  =  0

and the solutions are:  5,  -5