[cncbmb]

I have a question about 7f in the below question.

Original Problem



Solution:



How do we get to the last step annotated in red?




.
When I tried to solve for hydronium ion concentration, I got a very messy quadratic shown below so I do not think I am approaching this correctly.
The quadratic I got was this:

Let x=H3O+ concentration
x^2+(Ka-[NaOH]_total)x-Ka([HAc]_total-[NaOH]_total)=0

I also am getting a different numerical answer with this quadratic.