Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{k\arctan(x)}{x}-1\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for k (complex solution)
\left\{\begin{matrix}k=\frac{x\left(f+1\right)}{\arctan(x)}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{k\arctan(x)}{x}-1\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=\frac{x\left(f+1\right)}{\arctan(x)}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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xf=k\arctan(x)-x
The equation is in standard form.
\frac{xf}{x}=\frac{k\arctan(x)-x}{x}
Divide both sides by x.
f=\frac{k\arctan(x)-x}{x}
Dividing by x undoes the multiplication by x.
f=\frac{k\arctan(x)}{x}-1
Divide k\arctan(x)-x by x.
k\arctan(x)-x=fx
Swap sides so that all variable terms are on the left hand side.
k\arctan(x)=fx+x
Add x to both sides.
\arctan(x)k=fx+x
The equation is in standard form.
\frac{\arctan(x)k}{\arctan(x)}=\frac{fx+x}{\arctan(x)}
Divide both sides by \arctan(x).
k=\frac{fx+x}{\arctan(x)}
Dividing by \arctan(x) undoes the multiplication by \arctan(x).
k=\frac{x\left(f+1\right)}{\arctan(x)}
Divide xf+x by \arctan(x).
xf=k\arctan(x)-x
The equation is in standard form.
\frac{xf}{x}=\frac{k\arctan(x)-x}{x}
Divide both sides by x.
f=\frac{k\arctan(x)-x}{x}
Dividing by x undoes the multiplication by x.
f=\frac{k\arctan(x)}{x}-1
Divide k\arctan(x)-x by x.
k\arctan(x)-x=fx
Swap sides so that all variable terms are on the left hand side.
k\arctan(x)=fx+x
Add x to both sides.
\arctan(x)k=fx+x
The equation is in standard form.
\frac{\arctan(x)k}{\arctan(x)}=\frac{fx+x}{\arctan(x)}
Divide both sides by \arctan(x).
k=\frac{fx+x}{\arctan(x)}
Dividing by \arctan(x) undoes the multiplication by \arctan(x).
k=\frac{x\left(f+1\right)}{\arctan(x)}
Divide xf+x by \arctan(x).
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