Question

How do you solve `sqrt(x+9)-5=x+4` and find any extraneous solutions?

Answer 1

I found:
`x_1=-9`
`x_2=-8`
and no extraneous solutions.

Explanation:

We can write it as:
`sqrt(x+9)=x+4+5`
`sqrt(x+9)=x+9`
square both sides:
`x+9=(x+9)^2`
`x+9=x^2+18x+81`
`x^2+17x+72=0`
use the Quadratic Formula:
`x_(1,2)=(-17+-sqrt(289-288))/2=(-17+-1)/2`
`x_1=-9`
`x_2=-8`
Both works fine into the original equation.