Answer:
x = 14 is an extraneous solution
Step-by-step explanation:
[tex] 4\sqrt{x + 2} = -16 [/tex]
Divide both sides by 4.
[tex] \sqrt{x + 2} = -4 [/tex]
Square both sides.
[tex] (\sqrt{x + 2})^2 = (-4)^2 [/tex]
[tex] x + 2 = 16 [/tex]
[tex] x = 14 [/tex]
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:
[tex] 4\sqrt{x + 2} = -16 [/tex]
[tex] 4\sqrt{14 + 2} = -16 [/tex]
[tex] 4\sqrt{16} = -16 [/tex]
[tex] 4(4) = -16 [/tex]
[tex] 16 = -16 [/tex]
16 = -16 is a false statement, so the solution we found, x = 14, is an extraneous solution.
