Geometrically ...
x^2+(x+1)^2=4*(x/2)*(x+1)+1
Pictured above, x=6, which is even, and thus divisible by 2. Note: In general, either x is even or x+1 is even. Note: I didn't have enough light green Cuisenaire rods (3's), so I used 1's and 2's (whites and reds).