General approach to solving base resistor for a CE amplifier circuit that has no voltage divider at the base
Start with applying Kirchhoff's voltage law on the path shown:



In this loop only base current is unknown. Find it. 
Next, apply kirchhoff's voltage law in this loop:



Use, Emitter Current=Collector Current=beta*base current. 
Find voltage between Collector and Emitter. If the final result satisfies that the transistor is in active region your answer is correct. Otherwise proceed with the assumption of Saturation or cutoff region!