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x + sqrt(x - 2)  =  4

      sqrt(x - 2)  =  4 - x

[ sqrt(x - 2) ]²  =  [ 4 - x ]²

              x - 2  =  16 - 8x + x²

                   0  =  x² - 9x + 18

                   0  =  (x - 6)(x - 3)

 

Either  x = 6  or  x = 3

Actually, one of these is correct and the other one isn't  --  you'll need to check them to find the answer.