smc

The quadratic can also be written as $$x^2+\frac{8}{3}x+\frac{m}{2}$$ In order for the quadratic to be a square of a linear expression, the constant term must be the square of the x-term divided by 4. Thus, $$\frac{m}{2}=(\frac{8}{3}{)}^2\cdot \frac{1}{4}$$ $$\frac{m}{2}=\frac{16}{9}$$ $$m=\frac{32}{9}$$ The answer is $\boxed{3\text{ and }4}$.