A wire is stretched from the gound to the top of an antenna tower. The wire is 15 feet long. The height of the tower is 3ft greater than the distance d from the tower's base to the end of the wire. Find the distance and the height of the tower.
d^2 + (d + 3)^2 = 15^2
2 d^2 + 6d + 9 = 225 ... 2 d^2 + 6d - 216 = 0 ... d^2 + 3 d - 108 = 0
factoring ... (d + 12) (d - 9) = 0
d + 12 = 0 ... d = -12 ... negative value not realistic
d - 9 = 0 ... d = 9