Finding minimal polynomial of $\sqrt3 + i \sqrt 7$ over $\Bbb Q$

Question

$x=\sqrt 3 + i \sqrt 7$

I have come to the following polynomial: $x^4 + 8x^2+100=0$. By Eisenstein criterion, this pol is not irreducible in $\Bbb Q[x]$, but I don't know how to factor it further? Will be great if I can get some hints.