x^2 + 8x - 4 = 0.


You have these two terms x^2 + 8x . . . 
So, the thought which comes first to your mind is to get (x+4)^2.
To bring it to reality, you need to add 4^2 = 16 and to distract it to keep the balance.
Now, see how I do it below:


x^2 + 8x - 4 = 0

is equivalent to

(x^2 + 8x + 16) - 16 - 4 = 0

is equivalent to

 - 20 = 0

is equivalent to

 = 20

is equivalent to

x+4 = +/- 

is equivalent to

x = .


The two roots are  =   and   = .