Imogene wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11 in. by 14 in. piece of cardboard. She figures that for versatility the area of the bottom must be 80 in.^2. What size square should she cut from each corner?

Hint: Use the quadratic formula to solve for x.

(11-2x)(14-2x) = 80

(11-2x)(7-x) = 40

77 - 25 x + 2 x^2 = 40

2 x^2 - 25 x + 37 = 0

x = [ 25 +/- sqrt(625 - 296) ]/4

= [ 25 +/- 18.1 ] / 4

= 10.7, too big for sheet
or
= 1.73 ok

check
11 - 2(1.73 ) = 7.55
14 - 2(1.73 ) = 10.55
7.55 * 10.55 = 79.65 close enough to 80