Solve for m (complex solution)
m=-\frac{x}{x^{2}-2}
x\neq -\sqrt{2}\text{ and }x\neq \sqrt{2}
Solve for m
m=-\frac{x}{x^{2}-2}
|x|\neq \sqrt{2}
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{8m^{2}+1}-1}{2m}\text{; }x=-\frac{\sqrt{8m^{2}+1}+1}{2m}\text{, }&m\neq 0\\x=0\text{, }&m=0\end{matrix}\right.
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mx^{2}-2m=-x
Subtract x from both sides. Anything subtracted from zero gives its negation.
\left(x^{2}-2\right)m=-x
Combine all terms containing m.
\frac{\left(x^{2}-2\right)m}{x^{2}-2}=-\frac{x}{x^{2}-2}
Divide both sides by x^{2}-2.
m=-\frac{x}{x^{2}-2}
Dividing by x^{2}-2 undoes the multiplication by x^{2}-2.
mx^{2}-2m=-x
Subtract x from both sides. Anything subtracted from zero gives its negation.
\left(x^{2}-2\right)m=-x
Combine all terms containing m.
\frac{\left(x^{2}-2\right)m}{x^{2}-2}=-\frac{x}{x^{2}-2}
Divide both sides by x^{2}-2.
m=-\frac{x}{x^{2}-2}
Dividing by x^{2}-2 undoes the multiplication by x^{2}-2.
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