How do you do x ^4-4? what is the x values?

We know that
A difference of two perfect squares (A² - B²)  can be factored into  (A+B) • (A-B)
 then
x ^4-4> (x²-2)*(x²+2)
(x²-2)> (x-√2)*(x+√2)
x1=+√2
x2=-√2

the other term
(x²+2)=0-> x²=-2 x=(+-)√-2

i  is called the imaginary unit. It satisfies   i²  =-1
Both   i   and   -i   are the square roots of   -1 
√ -2  =√ -1• 2   = √ -1 •√  2   =i •  √ 2 
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x3=  0 + √2 i  
x4=  0  - √2 i 

the answer is 

the values of x are
x1=+√2
x2=-√2
x3=  0 + √2 i  
x4=  0  - √2 i