[AussieKenDoll]

What will be the pH if 0.010 0 mol of HA (with pKa =2.00) and 0.010 0 mol of A- are dissolved in water to make 1.00 L of solution?
See the attached pic for the answer to this question from Daniel C.Harris Quantitative Chemical Analysis book page 180
I don't understand how he solved for x? is there any approximation to consider or what?

[AWK]

The Henderson-Hasselbach equation gives approximately 5% concentration error for H₃O⁺ with a ratio c_acid/K_acid of about 500 and more (which is equivalent to the error of about 0.02 pH units). In this example, this ratio is equal to 1. Therefore, the author uses a different, but sufficient, simplification - it takes into account the dissociation of the acid, and ignore the autoprotolysis of water and the effect of ionic strength.
This simplification leads to a quadratic equation.