Solve for k
\left\{\begin{matrix}k=x+\frac{z}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.
Solve for x
x=\frac{\sqrt{k^{2}-4z}+k}{2}
x=\frac{-\sqrt{k^{2}-4z}+k}{2}\text{, }z\leq \frac{k^{2}}{4}
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-kx+z=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
-kx=-x^{2}-z
Subtract z from both sides.
\left(-x\right)k=-x^{2}-z
The equation is in standard form.
\frac{\left(-x\right)k}{-x}=\frac{-x^{2}-z}{-x}
Divide both sides by -x.
k=\frac{-x^{2}-z}{-x}
Dividing by -x undoes the multiplication by -x.
k=x+\frac{z}{x}
Divide -x^{2}-z by -x.
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