"With that I am almost done with my investigation."

Translation: Damit bin ich fast am Ende meiner Untersuchung.

[backtoschool]

No definitely not! I am a native German speaker. Your answer is perfectly right. You also could have said: "Damit bin ich fast fertig mit meiner Untersuchung/Nachforschung/Recherche." Feel free to ask, here are a lot of misinterpretations to be found and rectified, as well as sentences without a proper meaning. Nevertheless to program is good but it needs input from native speakers.

[Sk8rMom]

Danke. :-)

[Kelsieb]

I gave "Damit bin ich mit meiner Untersuchung fast
fertig" and it was accepted.

[Sk8rMom]

Is "Damit ist meine Untersuchung fast komplett" incorrect?

[CarolZaczk]

It clearly didn't like my "mit das", but instead of"damit" it suggested "hiermit". Haven't seen that one yet, is it closer to the meaning?

[gorelash]

It doesn't like Erforschung... Is that wrong?

[Weltfrieden]

I used fast erledigt instead of fast fertig and was marked incorrect, pretty sure it is acceptable but then again I'm not a native speaker. Anyone have input on that?

[backtoschool]

"erledigen" is used for everyday tasks which are easy can be done, should be done or have to be done. Mostly easy tasks they don’t consume much time and are not professional like your job.

You have have a task-list or to-do list and check them off, when done. That means as they are finished one after another you may state, "fished", "completed", "done" or in German = "erledigt" or "fertig" {damit}

This shows that "etwas erledigt haben", or "damit fertig sein" is not much of a difference.

In contrast if you work on a professional task like an:
investigation,
study,
your professional job,
recherché,
scientific work
writing a novel,

you wouldn't say "Ich habe das erledigt." but you would say:

"Ich bin fertig mit ...."
"Ich bin am Ende meiner(s) ..."
you may say:
"Ich habe meine Hausaufgaben erledigt"

Back to your question, I wouldn’t say it is wrong, but not the best word choice.