Answer
$-2\pm\sqrt {21}$
Work Step by Step
1. Based on the given conditions, we have $\vec v+\vec w=(x+2)i+2j$,
2. Use its magnitude, we have $\sqrt {(x+2)^2+2^2}=5$, thus $x^2+4x+8=25$ or $x^2+4x-17=0$
3. Thus we have $x=\frac{-4\pm\sqrt {16+4(17)}}{2}=-2\pm\sqrt {21}$
