Question

Find the solution of 3 times the square root of the quantity of x plus 5 equals negative 9, and determine if it is an extraneous solution

Answer 1

x = 4, it is an extraneous solution.

Explanation:

Translating the given statement, we get the following equation:

`3√((x+5)) =-9`

Dividing both sides by 3, we get:

`√((x+5)) =-3`

Now we will take square on both sides of the equation to get rid of the square root to get:

`(√((x+5)) )^2=(-3)^2`

So we are left with:

`x+5=9\\\\x=9-5\\\\x=4`

Therefore, the solution is 4.

Also, it is an extraneous solution because the equality is not met by substituting x = 4 in the original equation:

`3√((4+5)) =-9`

`3√((9)) =-9`

`3(3) =-9`

`9\\eq -9`