Solve for b
\left\{\begin{matrix}b=\frac{c^{2}}{2a}-\frac{a}{2}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&a=0\text{ and }c=0\end{matrix}\right.
Solve for a
a=\sqrt{b^{2}+c^{2}}-b
a=-\sqrt{b^{2}+c^{2}}-b
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2ab=c^{2}-a^{2}
Subtract a^{2} from both sides.
\frac{2ab}{2a}=\frac{\left(c-a\right)\left(a+c\right)}{2a}
Divide both sides by 2a.
b=\frac{\left(c-a\right)\left(a+c\right)}{2a}
Dividing by 2a undoes the multiplication by 2a.
b=\frac{c^{2}}{2a}-\frac{a}{2}
Divide \left(c-a\right)\left(c+a\right) by 2a.
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