Question

Find the solution of 5 times the square root of the quantity of x plus 7 equals negative 10, and determine if it is an extraneous solution

A) x = −3; extraneous

B) x = −3; not extraneous

C) x = 11; extraneous

D) x = 11; not extraneous

Answer 1

I took the test its x=-3; extraneous

Explanation:

Answer 2

The given equation is
`5√(x+7)=-10`

Squaring on both the sides of the equation, we get

`25(x+7)=100`

`x+7=4`

x = -3

An extraneous solution is a root of a transformed equation but it is not a root of the original equation.

Here x= -3 is also a root of the transformed equation but it is not a root of the original equation as we can see in the given equation

`5√(x+7)=-10`

As we put x = -3 in left hand side of the equation , we get

`5√(-3+7)= 5 * √(4) = 10` which is not equal to -10 that is the right hand side of the equation.

Therefore, x = -3 is an extraneous solution to the given equation.

So, Option B is the correct answer.