imc

$(x-2{)}^2$ = perfect square. 1 < perfect square < 25 Perfect square can equal: 4, 9, or 16 Solve for $x$: $(x-2{)}^2=4$ $x=4,0$ and $(x-2{)}^2=9$ $x=5,-1$ and $(x-2{)}^2=16$ $x=6,-2$ The sum of all integer solutions is $4+5+6+0+(-1)+(-2)=\boxed{12}$