Question

How do you solve `sqrt(x+2)-x=0`?

Answer 1

`x=2`

Explanation:

Rearrange to get the square root on one side on its own:
`sqrt(x+2)-x=0`
`sqrt(x+2)=x`

Square it out to get a quadratic:
`x+2=x^2`
`x^2-x-2=0`

Quadratic formula:
`x=1/2(1+-sqrt(1+8))`
`x=1/2(1+-3)`
`x=-1,2`

But when we square in our working we need to check that we haven't accidentally introduced extra roots. In this case we have: -1 is not a solution of the original equation, although 2 is.

So there is one solution: `x=2`.