Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{z}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{z}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-a^{-\frac{1}{2}}\sqrt{z}\text{; }x=a^{-\frac{1}{2}}\sqrt{z}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&z=0\text{ and }a=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\sqrt{\frac{z}{a}}\text{; }x=-\sqrt{\frac{z}{a}}\text{, }&\left(z\geq 0\text{ and }a>0\right)\text{ or }\left(z\leq 0\text{ and }a<0\right)\\x\in \mathrm{R}\text{, }&z=0\text{ and }a=0\end{matrix}\right.
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ax^{2}=z
Swap sides so that all variable terms are on the left hand side.
x^{2}a=z
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{z}{x^{2}}
Divide both sides by x^{2}.
a=\frac{z}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
ax^{2}=z
Swap sides so that all variable terms are on the left hand side.
x^{2}a=z
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{z}{x^{2}}
Divide both sides by x^{2}.
a=\frac{z}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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