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

1 Answer
Jun 17, 2018

Answer:

#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#.