Solve for z (complex solution)
\left\{\begin{matrix}z=\frac{e^{x}}{x}-\frac{x}{2}-\frac{1}{x}\text{, }&x\neq 0\\z\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for z
\left\{\begin{matrix}z=\frac{e^{x}}{x}-\frac{x}{2}-\frac{1}{x}\text{, }&x\neq 0\\z\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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zx+1=e^{x}-0.5x^{2}
Swap sides so that all variable terms are on the left hand side.
zx=e^{x}-0.5x^{2}-1
Subtract 1 from both sides.
xz=e^{x}-\frac{x^{2}}{2}-1
The equation is in standard form.
\frac{xz}{x}=\frac{e^{x}-\frac{x^{2}}{2}-1}{x}
Divide both sides by x.
z=\frac{e^{x}-\frac{x^{2}}{2}-1}{x}
Dividing by x undoes the multiplication by x.
z=\frac{e^{x}-1}{x}-\frac{x}{2}
Divide e^{x}-\frac{x^{2}}{2}-1 by x.
zx+1=e^{x}-0.5x^{2}
Swap sides so that all variable terms are on the left hand side.
zx=e^{x}-0.5x^{2}-1
Subtract 1 from both sides.
xz=e^{x}-\frac{x^{2}}{2}-1
The equation is in standard form.
\frac{xz}{x}=\frac{e^{x}-\frac{x^{2}}{2}-1}{x}
Divide both sides by x.
z=\frac{e^{x}-\frac{x^{2}}{2}-1}{x}
Dividing by x undoes the multiplication by x.
z=\frac{e^{x}-1}{x}-\frac{x}{2}
Divide e^{x}-\frac{x^{2}}{2}-1 by x.
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