See: List of castles, Castles in England, Castles in Scotland, Castles in Northern Ireland
Anglesey
Clwyd
Dyfed
Glamorgan
Gwent
Gwynedd
Powys
South Glamorgan
West Glamorgan
... left side is now a perfect square; it is the square of (x + b/(2a)). The right side can be written as a single fraction; the common denominator is 4a2. ...