The $\pi$-meson's mass is 139.57 MeV, and it decays into a muon and a neutrino. The muon has a mass of 105.4 5MeV, and a proper lifetime of $2.197 \times 10^{-6}$. The neutrino can be treated as massless in this process.
Assuming the $\pi$-meson decays at rest, what is the momentum of the muon?
Relevant equations from this resource: $$E_{\mu} = c^2 \left[ \frac{m_{\pi}^2 + m_{\mu}^2}{2m_{\pi}}\right] \tag{2.5}$$ $$E_{\mu} = \sqrt{p_{\mu}^2 c^2 + m_{\mu}^2 c^4}$$
I used the first equation and it gives about $E_{\mu}=9.866 \times 10^{18}$, then, used this value in the 2nd equation and solving for the momentum, I get a negative value under the square root, which doesn't make sense. In the 1st equation, the values I plugged in for $m_{\pi}$ and $m_{\mu}$ are just 139.57 and 105.47, and used $3 \times 10^8$ for $c$. Where did I go wrong?
The the first equation used here is based on the conservation of momentum. For the second equation, we know that $E^2 = p^2 c^2 + m^2 c^4$, so I took the square root of both sides to get $E$, and from there I tried to find the momentum $p_\mu$ using the mass of the muon and the energy $E_\mu$ of the muon found from the first equation.