Finding the load torque in a shunt DC motor

1. The problem statement, all variables and given/known data

Here is the question along with the solution. I am mainly concerned about part b).







2. Relevant equations

See image above.





3. The attempt at a solution

So instead, I decided to try to find the answer using the following formula:

P_in = P_{i^2 r} + P_Bm + P_out



This results in:

V_a(I_a+I_f) = I_a^2 R_a + I_f^2 R_f + 0.05P_out + P_out



Solving the above results in T_m = 10.461 which is slightly off compared to the actual solution, does anyone know why?