Answer:
it is not an extraneous solution.
Step-by-step 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.
[tex]4\sqrt{(x +2)} = -16[/tex]
Now let's solve this equation.
Divide both sides by 4, we get
[tex]\sqrt{(x+2)} = -4[/tex]
To get right of square root on the left hand side, square on both sides, we get
[tex](\sqrt{(x+2)})^2} = (-4)^{2}[/tex]
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
[tex]4\sqrt{(14 +2)} = -16[/tex]
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.
