Question 176011
Let x = side of the cut-out squares.

The length of the base is: 14 - 2x inches.
The width of the base is: 11 - 2x inches.

The area of the base is 80 in².

There is our equation:  (14 - 2x)(11 - 2x)  =  80

  and we have the quadratic:  2x² - 25x + 37  =  0

The Quadratic Formula gives us:  x  =  ¼(25 ± √239)

The smaller root is the answer:  x = ¼(25 - √329) ≈ 1.7154 inches

*[invoke solve_quadratic_equation 2, -25, 37]