I'm prepping for this math contest and I've been given notice that the special question is a magic square (this is Caribou Contest, they tell you on their website what the special question is a couple weeks prior so this should be legal). So naturally I decided to go take a look at what a magic square is. After a couple hours of solving a bunch them on the website I think I got a pretty good grasp on how to do them. However, when I tried to tackle the toughest difficulty setting on the website (Megaloceros) I was confronted by the problem: $$\begin{array}{|c|c|c|} \hline A & B & C \\ \hline -302 & D & E \\ \hline F & -128 & G\\ \hline \end{array} $$
I managed to find C by taking the average of -302 and -128 and got 215 so we have:
$$\begin{array}{|c|c|c|} \hline A & B & 215 \\ \hline -302 & D & E \\ \hline F & -128 & G\\ \hline \end{array} $$
Now that I got this, I was tempted to try solving this using a system of linear equations but I also wanted to find the "elegant" way to solve this.
Also if you know a general way to solve a magic square with negative numbers it would be greatly appreciated. I found on a similar question a general way to solve 3x3 magic squares if they had to be filled with the numbers {1...n^{2}}. However, this is not possible because there aren't enough spaces for consecutive numbers.
P.S. I don't know how to add spacing to make the magic squares columns align properly, sorry
P.P.S These magic squares have no limit to the size of the numbers, and they only use addition on the rows, columns, and diagonals