Solve for A (complex solution)
\left\{\begin{matrix}A\in \mathrm{C}\text{, }&\left(b=0\text{ or }b=1\right)\text{ and }x=0\\A=-\frac{\sqrt{b}\left(\sqrt{b}+1\right)}{2x}\text{; }A=-\frac{\sqrt{b}\left(\sqrt{b}-1\right)}{2x}\text{, }&x\neq 0\end{matrix}\right.
Solve for b (complex solution)
b=-2Ax+\frac{\sqrt{1-8Ax}}{2}+\frac{1}{2}
b=-2Ax-\frac{\sqrt{1-8Ax}}{2}+\frac{1}{2}
Solve for A
\left\{\begin{matrix}A\in \mathrm{R}\text{, }&\left(b=1\text{ or }b=0\right)\text{ and }x=0\\A=-\frac{\sqrt{b}\left(\sqrt{b}+1\right)}{2x}\text{; }A=-\frac{\sqrt{b}\left(\sqrt{b}-1\right)}{2x}\text{, }&x\neq 0\text{ and }b\geq 0\end{matrix}\right.
Solve for b
b=-2Ax+\frac{\sqrt{1-8Ax}}{2}+\frac{1}{2}
b=-2Ax-\frac{\sqrt{1-8Ax}}{2}+\frac{1}{2}\text{, }\left(x\geq 0\text{ or }A\geq \frac{1}{8x}\right)\text{ and }\left(x\leq 0\text{ or }A\leq \frac{1}{8x}\right)
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