900mm focal length / 10mm focal length = 90x
900mm focal length / 25mm focal length = 36x
If I understand correctly, Wade, the main effect of a barlow lenses is to optically change the focal length of the telescope. A 2x barlow makes yours a 1800mm focal length so the magnification obtained with an eyepiece doubles. If a 3x or 5x barlow, you can work it out. I expect you have a 2x barlow?
So the 10mm focal length eyepiece now gives 180x and the 25mm eyepiece now gives 72x.
Start experimenting with the 25mm and the barlow first. That should give you an idea of how it is performing without pushing the overall magnification up to far.
I suspect that 180x was maybe pushing the scope and conditions when you tried it. In my experience magnification is a bit like falling off a cliff. At some point it just goes plain ugly. On nights of great seeing I have pushed up to 450x. On other nights I leave the 2x and 3x barlows in the case! Nothing but mush!
Keep experimenting with Alpha Centauri until you can cleanly split the two close stars A & B. On nights of poor seeing, this can be difficult - their jelly blobs overlap too far. Also remember to wait until the star is well up in the sky. Around midnight at the moment. Then you are looking through a shorter column of horrible air.