Hi,



A = 

let x be the width of the border





 18 = (6-x)^2 = 36 - 12x +x^2

x^2  - 12x + 18 = 0

x = 1.75735931288072

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:

  

  

  

  For these solutions to exist, the discriminant  should not be a negative number.

  

  First, we need to compute the discriminant : .

  

  Discriminant d=72 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 10.2426406871193, 1.75735931288072.
Here's your graph:



  

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