# What's all this, then?

## Tschirnhausen transformations and the quartic

Here we show how a Tschirnhausen transformation can be used to solve a quartic equation. The steps are: Ensure the quartic is missing the cubic term, and its initial coefficient is 1. We can do this by first dividing by the initial coefficient to obtain an equation $x^4+b_3x^3+b_2x^2+b_1x+b_0=0$ and then replace the variable $$x$$ with $$y=x-b_3/ 4$$. This will produce a monic quartic equation missing the cubic term.

## Wrestling with Docker

For years I have been running a blog and other web apps on a VPS running Ubuntu 14.04 and Apache - a standard LAMP system. However, after experimenting with some apps - temporarily installing them and testing them, only to discard them, the system was becoming a total mess. Worst of all, various MySQL files were ballooning out in size: the ibdata1 file in /var/lib/mysql was coming in at a whopping 37Gb (39568015360 bytes to be more accurate).