The top of a 16-foot ladder is 2 feet farther up a wall than the foot is from the bottom of the wall. How far is the ladder from the bottom of the wall?

Let x=distance of foot of ladder from the wall, then

x+2=height of top of ladder up the wall.

length of ladder = 16 feet.

Using Pythagoras theorem,

x^2 + (x+2) ^2=16^2, expand and simplify

2x^2+4x+4 = 256 again simplify

x^2+2x-126=0 [fail to factor]

apply quadratic equation:

x = (-2+/-sqrt (4+504)) / 2

=-1+/-sqrt (127)

x=-12.3 (rejected) or

x=10.27 feet from wall.