# How do you solve #-4 sqrt(x+9) = 20# and find any extraneous solutions?

##### 1 Answer

#### Answer:

#### Explanation:

Your radical equation has **no solutions** for *real numbers*. Here's why.

Isolate the square root on one side of the equation by dividing both sides by

#(color(red)(cancel(color(black)(-4))) * sqrt(x+9))/color(red)(cancel(color(black)(-4))) = 20/(-4)#

#sqrt(x+9) = -5#

By definition, the square root of a **positive** real number must **always** produce a **positive** value. This implies that you must have

#x + 9 >= 0 -># you must take the square root of apositive numberwhen working in#RR#

#color(red)(cancel(color(black)(-5 >=0))) -># the square root of a positive numbermustbe apositive number

In your case ,*not* positive, which implies that your equation has **no solutions** when working in

You can have

You can write this as

#x in O/ -># no solutionsin#RR#