Mini Split Heat Pump

Looking for opinions on Mini Split Heat Pumps. I live in Southeastern Virginia. I had a 18 seer heat pump installed in my home in 2007. The home is very comfortable, except for the Master Bedroom addition. The addition is always really hot in the summer and very cold in the winter. We keep the house thermostat set to 73 in the winter, but the Master Bedroom stays at about 66 degrees. In the summer, it is usually about ten to 15 degrees hotter than the rest of the house. The addition size is 300sf.
I see an 18 seer mini split heat pump for about 1100. It is 9000 btu. Is that big enough for 300sf? It says it will only heat to about 15 degrees ambient because it doesn't have heat strips. How accurate is that 15 degree statement. We dont get many days at 15 degrees here, but we get quite a few at 25 to 35. I would hat to buy this thing and it is not able to maintain the bed room at 73 in the winter.
As a side note, I am in a HVAC program at my local community college. I want to use this install as a learning project. I will try to do most of the install myself, and I will get my instructor to come out for the lineset evac and start up.
Any advice would be welcome.
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I would investigate making the system you have work before deciding to add another system. You didn't give us a lot of info on the specifics of the system you have. Are the runs from the sstem to the mb particularly long? Some years back I made significant improvements to our bonus room, which also ran cool in winter amd hot in summer, simply by replacing the r4 6" fle lines to it with r6 8" lines. Today you can get r8 flex. As others have noted you can also add insulation. Any omprovements you can make wiht passive solutions will have no future costs. Adding another heat pump will cost you to run it and will have maintenance costs as well.
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Agreed, adding extra heating will not help since there is obviously poor air circulation reaching the master bedroom. Adding more heating will just heat up the other rooms even more when you bring the bedroom up to where you want. Your heating/cooling class should be teaching that.
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