Problem with 2 radicals

[jtw2e2]

My difficulty with this problem is the x which is under the "top" radical but not under the interior radical.
My first thought was to square both sides, giving me:

?(x-5) +x = 25

Then I tried to square both sides again to get rid of the remaining radical, and FOILing left me with a mess. I eventually
worked to get x(x +2x?(x-5) +1) = 620. I really think I've just made the problem more difficult.
Some pointers in the right direction would be much appreciated! Thank you.

-Jeff

 

[Loren]

Your first step was good. Next, isolate the remaining radical by doing whatever is necessary to move any term(s) not under the radical sign to the other side of the equation. Then, square both sides.

 

[jtw2e2]

Your first step was good. Next, isolate the remaining radical by doing whatever is necessary to move any term(s) not under the radical sign to the other side of the equation. Then, square both sides.

Thanks for the help. I think I've got it:

x-5 = x^2 - 50x + 625
0 = x^2 - 51x + 630
0 = (x - 21)(x-30)

x = 21

(x=30 does not appear to be a real solution.)