Solve for E
E=\frac{x-1}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{1-4E}+1}{2E}\text{; }x=\frac{-\sqrt{1-4E}+1}{2E}\text{, }&E\neq 0\\x=1\text{, }&E=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{1-4E}+1}{2E}\text{; }x=\frac{-\sqrt{1-4E}+1}{2E}\text{, }&E\neq 0\text{ and }E\leq \frac{1}{4}\\x=1\text{, }&E=0\end{matrix}\right.
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Ex^{2}+1=x
Add x to both sides. Anything plus zero gives itself.
Ex^{2}=x-1
Subtract 1 from both sides.
x^{2}E=x-1
The equation is in standard form.
\frac{x^{2}E}{x^{2}}=\frac{x-1}{x^{2}}
Divide both sides by x^{2}.
E=\frac{x-1}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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