TRACON Controller failed to make a required hand off to a Center Controller when electing to continue to work an aircraft outside his/her airspace for 25 miles.

Narrative

I accepted the hand off on a BE99 north of our airspace at 7;500. After initial contact the BE99 advised they were climbing to 9;500. I coordinated with the Center Sector that had handed them off and whose airspace they were still in that I would keep control and communication with the aircraft and hand them off to the next Center Sector when appropriate. I spaced it out and did not complete a hand off prior to the aircraft entering the next controllers airspace. Traffic was very slow; this was the only aircraft on frequency. Although at first I correctly identified that I would need to hand off the aircraft halfway across the lateral confines of my airspace; I forgot and was thinking I had thirty miles before needing to hand them off. Recommendation; I violated one of my own rules: work the aircraft in your own airspace. Once the aircraft informed me they would be climbing above my airspace I should have handed them back to the Center sector that gave them to me and whose airspace they would be in for 25 miles.