Question

Find the solution of 4 times the square root of the quantity of x plus 2 equals negative 16, and determine if it is an extraneous solution.

Answer 1

`4 √(x+2) =16\\ √(x+2) = (16)/(4)=4\\x+2=4^2=16\\x=16 - 2 = 14`
Solution is x = 14
Solution is not extraneous.

Answer 2

it is not an extraneous solution.

Explanation:

Given: "4 times the square root of the quantity of x plus 2 equals negative 16"

Let's convert the given verbal equal to algebraic equation.

`4√((x +2)) = -16`

Now let's solve this equation.

Divide both sides by 4, we get

`√((x+2)) = -4`

To get right of square root on the left hand side, square on both sides, we get

`(√((x+2)))^2} = (-4)^(2)`

On the left hand side, the square root will get canceled.

(x +2) = 16

To find the value of x, subtract 2 on both sides, we get

x + 2 - 2 = 16 - 2

x = 14

To find whether it is extraneous solution or not, let's go back to the original equation and substitute x = 14

`4√((14 +2)) = -16`

4√16 = -16

4*±4 = -16

4 *4 = 16

4*-4 = -16

We get -16 as solution for the given equation.

Therefore, it is not an extraneous solution.