<s>[INST] Solving the equation $x + \sqrt{2x+1} = 7$ I can't solve 

$x + \sqrt{2x+1} = 7$.

Well, I know the answer is 4, but that is from just reasoning it out. I can't algebraically solve it.
Thus, a step by step is what I really need.
Thanks in advance!!
 [/INST] $7-x= \sqrt{2x+1}$
$ (7-x)^2 = 2x+1$
$ x^2-14x+49 = 2x+1 $
$x^2-16x+48=0$
$(x-8)^2-64+48=0$
$(x-8)^2=16$
$x-8=\pm 4$
$x=12$ or $x=4$
But $x=12$ does not work in the original equation. So the answer is $x=4$.
(Or the original equation requires $7-x\ge 0$ and so $x\le 7$.)
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