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

Your wording amounts to the equation
4*sqrt(x)+2=-16
4*sqrt(x)=-18
sqrt(x)=-9
but square roots are nonnegative so no solution exists.

Answer 2

Solution is x = 14

Solution is not extraneous.