Answer:
He failed to check for extraneous solutions
Explanation:
sqrt(x+6) -4 =x
Add 4 to each side
sqrt(x+6) -4+4 =x+4
sqrt(x+6) =x+4
Sqaure each side
(sqrt(x+6))^2 =(x+4)^2
x+6 = x^2 +8x+16
Subtract 6 from each side
x = x^2 +8x +10
Subtract x from each side
0 = x^2 +7x +10
Factor
0 = (x+5) (x+2)
Using the zero product property
x=-5 x=-2
Check the solutions
sqrt(-5+6) -4 =-5
sqrt(1) -4 = -5
1-4 =-5
-3 does not equal -5 not a solution
sqrt(-2+6) -4 =-2
sqrt(4) -4 = -2
2-4 =-2 is a solution