Isn't it simply adding up momentum vector of M1, and momentum vector of M2 then the
resultant will be momentum of M3?

If so, then you get a right angle triangle.

You know momentum of both sides and just by using pythagoras you can find
momentum of M3, then just divided by the mass then you can get the velocity right?

Sorry I did not notice your formula M3 = Mtotal - (M1+M2) before. I wanted to say the same - you should subtract the resultant of M1 and M2 from Mtotal to get M3, and I ment that Mtotal is momentum of the bullet before exploding.

The total momemtum which is equal to the momentum the bullet had just before the explosion is 32*215i as the piece moves along the positive x axis. The momentum of the 7 kg piece is 7*310j as the piece moves along the positive y axis. The momentum of the 4.5 kg piece is -4.5*370i.
The sum of the x components is the same before and after explosion, and the same holds for the y components.
32*215=M3x-4.5*370
0=M3y+7*310.
Calculate the components of M3. Determine the magnitude and divide by the mass of the third piece to get the speed as you have written down in your first letter.
ehild