If the problem is: √(x + 4) = x - 2:
Square both sides: x + 4 = (x - 2)2
Simplify: x + 4 = x2 - 4x + 4
Solving: 0 = x2 - 5x
Factoring: 0 = x(x - 5)
So: 0 = x or 0 = x - 5
Answers: x = 0 or x = 5
Checking: when x = 0: √(x + 4) = x - 2 ---> √(0 + 4) = 0 - 2
---> √(4) = - 2 ---> 2 = -2 <--- Impossible!
when x = 5: √(5 + 4) = 5 - 2 ---> √(9) = 3 <--- This works!
If the problem is: √(x + 4) = x - 2:
Square both sides: x + 4 = (x - 2)2
Simplify: x + 4 = x2 - 4x + 4
Solving: 0 = x2 - 5x
Factoring: 0 = x(x - 5)
So: 0 = x or 0 = x - 5
Answers: x = 0 or x = 5
Checking: when x = 0: √(x + 4) = x - 2 ---> √(0 + 4) = 0 - 2
---> √(4) = - 2 ---> 2 = -2 <--- Impossible!
when x = 5: √(5 + 4) = 5 - 2 ---> √(9) = 3 <--- This works!