Question

Find the solution of ___ and determine if it is an extraneous solution

Answer 1

Answer:

x = 14 is an extraneous solution

Step-by-step explanation:

$4\sqrt{x + 2} = -16$

Divide both sides by 4.

$\sqrt{x + 2} = -4$

Square both sides.

$(\sqrt{x + 2})^2 = (-4)^2$

$x + 2 = 16$

$x = 14$

Since we squared both sides, we much check for extraneous solutions because the process of squaring both sides can introduce extraneous solutions.

Check x = 14:

$4\sqrt{x + 2} = -16$

$4\sqrt{14 + 2} = -16$

$4\sqrt{16} = -16$

$4(4) = -16$

$16 = -16$

16 = -16 is a false statement, so the solution we found, x = 14, is an extraneous solution.