sq. rt. (x-7) + sq. rt. (x) =4
$\displaystyle \sqrt{x - 7} + \sqrt{x} = 4$
The trick here is to divide and conquer. You want to isolate one of the square roots on one side of the equation. So:
$\displaystyle \sqrt{x - 7} = 4 - \sqrt{x}$ <-- Square both sides
$\displaystyle x - 7 = \left ( 4 - \sqrt{x} \right ) ^2$
$\displaystyle x - 7 = 16 - 8\sqrt{x} + x$
Now do it again:
$\displaystyle \sqrt{x} =\frac{23}{8}$
$\displaystyle x = \left ( \frac{23}{8} \right ) ^2 = \frac{529}{64}$
Always always always check your solutions in the original equation:
$\displaystyle \sqrt{\frac{529}{64} - 7} + \sqrt{\frac{529}{64}} = 4$
$\displaystyle \sqrt{\frac{81}{64}} + \frac{23}{8} = 4$
$\displaystyle \frac{9}{8} + \frac{23}{8} = 4$
$\displaystyle \frac{32}{8} = 4$
$\displaystyle 4 = 4$ (Check!)
-Dan