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

1 Answer
Jun 17, 2018

x=2x=2

Explanation:

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

Square it out to get a quadratic:
x+2=x^2x+2=x2
x^2-x-2=0x2x2=0

Quadratic formula:
x=1/2(1+-sqrt(1+8))x=12(1±1+8)
x=1/2(1+-3)x=12(1±3)
x=-1,2x=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=2x=2.