jmc

We use the fact that the sum and product of the roots of a quadratic equation $a{x}^2+bx+c=0$ are given by $-b/a$ and $c/a$, respectively. Letting the solutions to the given equation be $p$ and $q$, we have $p+q=-4/2=-2$ and $pq=-1/2$, so the answer is $p^2+q^2=(p+q{)}^2-2pq=(-2{)}^2-2(-1/2)=\boxed{5}$.