## Deriving the quadratic formula

### November 1, 2014

This afternoon I decided to practice completing the square (I’m afraid that I’m rediscovering my inner nerd and am now studying for a math degree). After a few examples, I decided to go a bit more general and derive the quadratic formula. I guess that doing things like this is something which I’m going to have to get used to.

I figured that this is also a good excuse to practice my skills and write it out.

We want to find the general solution of the equation:

Start off by dividing through by

then complete the square

rearrange to leave the square on the left

simplify the RHS

take the square root of both sides

simplify the RHS

make the subject

and, boom – the quadratic formula!

If I could go back in time and tell my younger self one thing, it would be to play with maths – don’t just do the homework. It’s all very well being able to follow a process (and essentially being a calculator), but knowing and understanding where something comes from unearths the true beauty of maths.