Any math guys out there?

 
Saw this at the bottom of a page about Chris Cornell and decided to solve it.  However, my solution didn't check out going the other way and, since it's been many years I'm wondering where I went wrong.
 
1)  To get rid of the square root symbols I squared both sides so now the equation reads (x + 15) + x = 225
2)  Subtract 15 from both sides to get x + x = 210, or 2x = 210
3)  Divide both sides by 2 to get x = 105
 
However, checking the answer shows that x has to be smaller than 105.
 
1)  The square root of 120 (105 + 15) is 10.95+
2)  The square root of 105 is 10.25+
3)  Obviously 10.95 + 10.25 is greater than 15...
 
Working it the other way by plugging in a few examples got me the real answer fairly quick (x = 49), but I'm trying to figure out where I did the normal solving wrong.
 
Solution:  
 
1)  The square root of (49 + 15) + the square root of 49 = 15
2)  The square root of 64 + the square root of 49 = 15
3)  8 + 7 = 15

There's two mush X in the ecwayshun.

In other words you don’t separate the √ X + 15  and √ X 
… but put brackets around it and square the whole thing.
√ X + 15  + √ X  = 15
(√ X + 15  + √ X  )² = 15²

I just did it by moving the √ X  other side of the equation before squaring.
 
- note that I can't get a top on the square root thingy so you will have to use your imagination and picture the x+15 under the square root thingy.

No one told me there would be math.