linear algebra - Complex roots of a 4th degree polynomial

I am trying to find the roots of $w(x)=x^4+x^2+169$. I am able to simplify this to $(x^2+5-12i)(x^2+5+12i)$. I also know how to solve both expressions using a formula for the square root of a complex number. This seems very tedious. Is there a quicker way? Also, is there a quick way to write down the original polynomial as a product of polynomials with $deg \le 2$?

Answer

$$x^4+x^2+169=(x^2+13)^2-25x^2=0$$
hence
$$(x^2+13-5x)(x^2+13+5x)=0$$