pH of very dilute acids

From doing some research on the site I have found that many people have posted about solutions of $\ce{HCl}$ where $[\ce{HCl}] = \pu{1e-8 mol dm-3}$

Here they are able to deduce

$$[\ce{H+}] = \frac{[\ce{HCl}]_0}{2} + \sqrt{\frac{[\ce{HCl}]_0^2}{4} + K_\mathrm{w}}$$

where $[\ce{HCl}]_0$ is the initial concentration of $\ce{HCl}$ dissolved.

Can we make a generalisation of this and say if $\ce{H_xA}$ is a strong acid that will dissociate fully when dissolved in water? Then if $[\ce{H_xA}]_0 < \sqrt{K_\mathrm{w}}$ then the $\mathrm{pH}$ of solution can be expressed by

$$\mathrm{pH} = -\log_{10} \left(\frac{x[\ce{H_xA}]_0}{2} + \sqrt{\frac{(x[\ce{H_xA}]_0)^2}{4} + K_\mathrm{w}}\right)$$