Working on the fast computation of BS implied volatility. I have read some papers regarding the explicit formula ofr BS IV. Like the Li(2005) paper: A new formula for computing implied volatility. However, I met a very serious problem in their formulas because the terms in the square root bracket can goes to negative is the option price is small enough, the simple formula by Corrado and Miller(1996) also suffers from the same problem. How can I solve this problem?

BTW, the explicit formula only serves as the initial guess for the subsequent numerical methods.

I don't know how to insert image for the formula, sorry.