Question

√(x+2) -7 =√(x+9)

Answer 1

are we solving?

If so, then ....
square both sides
x+2 - 14√(x+2) = x+9
- 14√(x+2) = 7
- 2√(x+2) = 1
(at this point I can tell that this cannot have a solution.
Can you see why? )

but let's carry on
square again
4(x+2) = 1
4x = -7
x = -7/4

check:
if x=-7/4
LS = √(-7/4 + 2) - 7
= √(1/4) - 7
= 1/2 - 7 = -13/2
RS = √(-7/4+9) = √29/4) ≠ LS

no solution