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:
Pin = Pi^2 r + PBm + Pout

This results in:
Va(Ia+If) = Ia^2 Ra + If^2 Rf + 0.05Pout + Pout

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

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