Question

How do you solve `a^2=4a`?

Answer 1

See below.

Explanation:

With quite some care!

Good practise is to re-write it as follows:

`a^2 = 4 a`

`implies a^2 - 4 a = 0`

And then factor it:

`implies a(a - 4) = 0`

So now you know that you have two solutions, ie `a = 0` and `a = 4`.

The temptation here, which exists all the way up the maths tree (to my branch, at least!), is to cancel out the `a` terms, ie to say that `a^2 = 4 a implies a = 4`.

But that just throws away a solution :(

Zero is every bit as scarey as infinity, perhaps even scarier!