An implied volatility solver that cannot fail

You have bs_call(S, K, T, r, sig), which returns the Black-Scholes call price and vega. Plain Newton from $\sigma_0 = 20\%$ works for at-the-money options but fails for $S = 100$, $K = 150$, $T = 0.25$, $r = 0$ and a quoted price of $1.486$.

Explain why it fails, then write implied_vol(price, S, K, T, r) that returns the implied volatility whenever one exists. Which inputs should it reject?