Analytic or Analytical?

Merriam-Webster's lists analytic as a main entry but also makes note that analytical is a variant. So do a couple of other online dictionaries I checked.
Whenever I type in analytical in a Word document or try googling it, however, the term is flagged with a red squiggly underline (in fact, the same thing is happening as I write this post).
Is this one of those words that is not technically correct but has somehow become acceptable through repeated use?
I am formulating a cover letter and resume and want to ensure that I use the right word in a general description of my qualifications and skills, so I'd be so very grateful for the feedback of my peers on this forum. Thank you.