Question 426919
Your approach is right.  But the area of the rectangle is actually (X+4)(X+14)=936 because you have to add 2 inches to each side to form a 2-inch border. Thus we have:
 
(X+4)(X+10+4)=936
(X+4)(X+14)=936
X^2 + 18X + 56 = 936
X^2 + 18X - 880 = 0
(X+40)(X-22) = 0
X = -40 or 22

We reject the negative answer, and we're left with X = 22.  If we check this we get (22+4)(22+14)= 936, 26*36 = 936, 936 = 936.

Edited 3-13-2017
x * x+10=936
x²+10x-936=0
(x+36)(x-26)=0
x=-36 or 26
x+10=36
The dimensions of the entire picture and frame is 36" x 26". The dimensions of the picture itself is (36-4)x(26-4), or 32" by 22". ☺☺☺☺