Solve sqrt{x}+sqrt{2a-x}=a

$$\sqrt { x } + \sqrt { 2 a - x } = a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\sqrt{-x+2\sqrt{x}+1}+\sqrt{x}+1\text{; }a=\sqrt{-x+2\sqrt{x}+1}+\sqrt{x}+1\text{, }&arg(a-\sqrt{x})<\pi \\a=\frac{x}{2}\text{, }&x=4\text{ or }x=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\left(-\sqrt{a\left(4-a\right)}+a\right)^{2}}{4}\text{; }x=\frac{\left(\sqrt{a\left(4-a\right)}+a\right)^{2}}{4}\text{, }&arg(\frac{\sqrt{a\left(4-a\right)}+a}{2})<\pi \text{ and }arg(\frac{-\sqrt{a\left(4-a\right)}+a}{2})<\pi \\x=0\text{, }&\left(a=0\text{ and }\text{Indeterminate}<\pi \right)\text{ or }a=2\\x=a^{2}\text{, }&a=2\text{ or }a=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\sqrt{-x+2\sqrt{x}+1}+\sqrt{x}+1\text{, }&x\leq 2\sqrt{2}+3\text{ and }x\geq 0\text{ and }x\leq 2\sqrt{-x+2\sqrt{x}+1}+2\sqrt{x}+2\\a=-\sqrt{-x+2\sqrt{x}+1}+\sqrt{x}+1\text{, }&x=0\text{ or }\left(x\leq -2\sqrt{-x+2\sqrt{x}+1}+2\sqrt{x}+2\text{ and }x\leq 2\sqrt{2}+3\text{ and }x\geq 4\right)\end{matrix}\right.$$

Solve for x

$$x=\frac{a\left(-\sqrt{a\left(4-a\right)}+2\right)}{2}$$

$$x=\frac{a\left(\sqrt{a\left(4-a\right)}+2\right)}{2}\text{, }a=0\text{ or }\left(a\geq 2\text{ and }a\leq 4\right)$$