Suppose a rectangle has an area of 90m^{2} and the sides are x+1 and x+2. Find the dimensions of the rectangle.
(x+1)·(x+2)=90
x^{2}+3x+2=90
x^{2}+3x-88=0
(x+11)·(x-8)=0
x+11=0; x=-11
x-8=0; x=8
The sides are 9m and 10m long.

We have a square of cardboard with which we want to make a box (without cover-up) of 363 cm^{3}. In order to do this we cut away four squares with sides of 3 cm from the corners of the cardboard. What length were the sides of the original square of cardboard?