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

Feb 14, 2017

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:

$\implies a \left(a - 4\right) = 0$

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!