Let z and w be complex numbers such that

Question

|2z-2|=25,
|z+2w|=5, and
|z+w|=2.

Find |z|.

I first squared both equations and expressed the square of the magnitudes in terms of the complex numbers and its conjugates. Next, I summed the equations together and attempted to solve for |z|.

My equation got very messy very quickly and if there is an easier way to go about doing this. Any help would be very much appreciated!