How badly will a C in a dual enrollment class hurt my admissions chances?

So is Georgia Tech part of your high schools' dual enrollment program or is this something you did on your own outside of school to boost your course rigor?

If the grade C get reported back to your HS and appears on your official transcript, then there is nothing you can do about it except write about it in the add'l information section. You can explain that you got ahead of your skis and thought you were well prepared for this college level math course but in fact found yourself struggling just to pass the course. I thinks it better to err and ask for forgiveness rather than not to take any risks and chances in life.

In comparison to your HS coursework, did you succeed in any other dual enrollment classes or other online college courses? Or is this the only one you ventured to enroll in?

Context is everything so that's why I'm asking. If you took 5 DE classes and got 4 As and this C, then you are showing you are well prepared for college classes. But if you only took a single DE class and got a C, then applying to a top STEM research university will be challenging unless you can show them evidence of success in other high level STEM classes you took both in and outside of HS. If you took 8-10 APS and got As in them the mostly 4s and 5s on the AP exams and those included AP Calc BC, AP Physics 1,2 C, and AP Chem, AP Bio etc, then you are showing evidence that you are prepared for the course rigor at schools like Rice an NW.

Since very little information is revealed in your question about the full body of your academic narrative, I recommend that you conduct a full inventory of every class you took and add up all the APs, IBs, College courses (whether direct enrollment or dual enrollment) and any other rigorous self-study or summer programs and/or internships and determine how you compare to the typical admit at Rice or NW.

https://www.youtube.com/watch?v=qML2UQOx10k

Good luck.