I know there are a lot of smart people on here.

Can anybody explain to me how to get this...?

Point P lines on the x axis. The coordinates of A and B. are (0, 6) and (0, -15) respectively. The sum of the distances of PA and PB is 27 units. Determine the possible coordinates of P.

I got (8, 0) (-8, 0), but did it with trial and error.

Respect to those who can get this.