Conservation of Energy and Momentum of Particles

[Fanman22]

An atomic nucleus initially moving at 500 m/s emits an alpha particle in the direction of its velocity, and the new nucleus slows to 480 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 226 u, what speed does the alpha particle have when it is emitted?

Well this is what I came up with so far:
m1=226 V1=500 V1'=?
m2=4 V2=? V2'=480

Use Conservation of Momentum and conservation of kinetic energy to get these equations, respectively:

226(500) + 4(V2) = 226(V1') + 4(480) and...

.5(226)(500)^2 + .5(4)(V2)^2 = .5(226)(V1')^2 + .5(4)(480)^2

Hopefully this is correct so far...now I know I'm supposed to do substitution next, but I'm having some algebra problems.

I got V2= -2.77e4 + 56.5(V1')
I'm not sure if this is correct I'm ashamed to say it, but I'm having a lot of trouble doing the algebra after I substitute it into the other equation.

 

[Doc Al]

Energy is not conserved. All you need is conservation of momentum. Realize that after the decay the old nucleus (226u) becomes two particles: the alpha particle (4u) and a new, smaller nucleus (222u).

 

[Fanman22]

Thanks, my brain just isn't working anymore. I spend about 45minutes trying to do a ridiculous substitution method. You guys are saviors.