A $1\mathrm{.}00L$ flask is filled with $0\mathrm{.}500$molHI at $448C,$ and $K_c=50.$ for hydrogen gas reacting

with iodine gas at this temperature. Determine the concentrations of $H_2,I_2,$ and $HI$ at

equilibrium. $($You need not use the quadratic equation to solve this problem$)$