Solve for R (complex solution)
\left\{\begin{matrix}R=\frac{y^{2}}{x}+x\text{, }&x\neq 0\\R\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for R
\left\{\begin{matrix}R=\frac{y^{2}}{x}+x\text{, }&x\neq 0\\R\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
x=\frac{\sqrt{R^{2}-4y^{2}}+R}{2}
x=\frac{-\sqrt{R^{2}-4y^{2}}+R}{2}
Solve for x
x=\frac{\sqrt{R^{2}-4y^{2}}+R}{2}
x=\frac{-\sqrt{R^{2}-4y^{2}}+R}{2}\text{, }|y|\leq \frac{|R|}{2}
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Rx=x^{2}+y^{2}
Swap sides so that all variable terms are on the left hand side.
xR=x^{2}+y^{2}
The equation is in standard form.
\frac{xR}{x}=\frac{x^{2}+y^{2}}{x}
Divide both sides by x.
R=\frac{x^{2}+y^{2}}{x}
Dividing by x undoes the multiplication by x.
R=\frac{y^{2}}{x}+x
Divide x^{2}+y^{2} by x.
Rx=x^{2}+y^{2}
Swap sides so that all variable terms are on the left hand side.
xR=x^{2}+y^{2}
The equation is in standard form.
\frac{xR}{x}=\frac{x^{2}+y^{2}}{x}
Divide both sides by x.
R=\frac{x^{2}+y^{2}}{x}
Dividing by x undoes the multiplication by x.
R=\frac{y^{2}}{x}+x
Divide x^{2}+y^{2} by x.
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