calculus - simple limit but I forget how to prove it

I have to calculate the following limit

$$\lim_{x\rightarrow -\infty} \sqrt{x^2+2x+2} - x$$

it is in un undeterminated form.

I tried to rewrite it as follows:

$$\lim_{x\rightarrow -\infty} \sqrt{x^2+2x+2} - \sqrt{|x|^2}$$

but seems a dead road.

Can anyone suggest a solution?

thanks for your help