Solve for x from $\sqrt{x - 7} - \sqrt{x} = 1$.

$\sqrt{x - 7} - \sqrt{x} = 1$

$\sqrt{x - 7} = 1 + \sqrt{x}$

$x - 7 = (1 + \sqrt{x})^2$

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

$-8 = 2\sqrt{x}$

$-4 = \sqrt{x}$

$x = 16$
 

Checking
$\sqrt{16 - 7} - \sqrt{16} = -1$   ←   not okay

$-\sqrt{16 - 7} - (-\sqrt{16}) = 1$   ←   check
 

Answer is x = 16
 

Another Solution
Use CALC function

No value of X from the choices will result to 1.

X = 16 will result to 1

Answer: x = 16