Don't you mean when Ka is far from 1?
The real answer is that you can ignore it if it doesn't change any significant figure in the concentration of the weak acid. If you have Ka = x^2/[HA]-x, then you can ignore the -x if it doesn't affect [HA]. E.g. if your initial concentration was 1.00, and x came out to be 0.00001, then 1.00 - 0.00001 = 1.00, so you can ignore it. My recommendation is to ignore it and then back-substitute it to see if it produces any deviation.
I don't quite know what you mean by using the quadratic formula, but let me give you one tricky question. What is the pH of 10^-8 M solution of HCl?