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

1 Answer
Gió
Jun 26, 2016

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.

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