An extraneous solution is a solution/value obtained while solving the equation but once evaluated is not a valid solution (meaning the value makes the equation false)
To check for extraneous solutions, we must plug in #0# and #-3# for #x# separately and evaluate. What we are essentially looking for, is to see if both sides of the equation are equal or not. If not, then the solution is extraneous.
For #x=0#
#sqrt(4-2(0)-(0)^2)=(0)+2#
#sqrt4=2#
#2=2# This equation is true since both sides of the equation are equal meaning this is NOT an extraneous solution.
For #x=-3#
#sqrt(4-2(-3)-(-3)^2)=(-3)+2#
#sqrt(4+6-9)=-1#
#sqrt1=-1#
#1!=-1# This equation is false since both sides of the equation are different. Therefore, #x=-3# IS an extraneous solution
