4. (4 points) Determine all values of the parameter $a$ for which the equation $x+\sqrt{a-x^{2}}=1$ has two distinct solutions.
4. For $a \in\left(\frac{1}{2} ; 1\right]$ the equation has two distinct solutions.

$+(4$ points) - the solution is correct.

+- (3 points) - the solution is generally correct, but there are minor inaccuracies in selecting the parameter values.

-+ (2 points) - the roots $x=\frac{1 \pm \sqrt{2 a-1}}{2}$ were found, but the different cases of parameter values were analyzed incorrectly.