Think of the 13-ft length of the ladder as the hypotenuse of a right triangle. Represent the horiz. distance from foot of ladder to base of tree by x, or 5 ft.
Represent the vert. dist. from base of tree to top of ladder by y, which is unknown.
Then (13 ft)^2 = (5 ft)^2 + y^2, or
169 ft^2 = 25 ft^2 + y^2. This simplifies to y^2 = 144. Thus y = + 12 feeet.
Note: Please pay attention to your spelling: "lader i up agenst a tree" should be "the top of a 13-ft ladder is placed against a tree."
Multiply 1.275 with 51 to get the answer (65.025)
Group x terms
(2x^2+8x)-12=0
undistribute 2
2(x^2+4x)-12=0
take 1/2 of 4 and square it, add negative and positive of it insde (2^2=4)
2(x^2+4x+4-4)-12=0
factor perfect square
2((x+2)^2-4)-12=0
distribute
2(x+2)^2-8-12=0
2(x+2)^2-20=0
add 20 to both sides
2(x+2)^2=20
divide both sides by 2
(x+2)^2=10
sqrt both sides, remember to take positive and negative root
x+2=+/-√10
minus 2 both sides
x=-2+√10 and -2-√10
