Question
Solve the following equation: $10 x -\frac{1}{ x }=3$
✓
Answer
$10 x -\frac{1}{ x }=3$
$ 10 x ^2-1=3 x $
$10 x ^2-3 x -1=0 $
$ x ^2-\frac{3}{10} x -\frac{1}{10}=0$
$ x ^2+\frac{1}{5} x -\frac{1}{2} x -\frac{1}{10}=0$
$ x \left( x +\frac{1}{5}\right)-\frac{1}{2}\left( x +\frac{1}{5}\right)=0$
$\left( x +\frac{1}{5}\right)\left( x -\frac{1}{2}\right)=0 $
$ \left( x +\frac{1}{5}\right)=0,\left( x -\frac{1}{2}\right)=0 $
$ x =-\frac{1}{5}, x=\frac{1}{2}$
$ 10 x ^2-1=3 x $
$10 x ^2-3 x -1=0 $
$ x ^2-\frac{3}{10} x -\frac{1}{10}=0$
$ x ^2+\frac{1}{5} x -\frac{1}{2} x -\frac{1}{10}=0$
$ x \left( x +\frac{1}{5}\right)-\frac{1}{2}\left( x +\frac{1}{5}\right)=0$
$\left( x +\frac{1}{5}\right)\left( x -\frac{1}{2}\right)=0 $
$ \left( x +\frac{1}{5}\right)=0,\left( x -\frac{1}{2}\right)=0 $
$ x =-\frac{1}{5}, x=\frac{1}{2}$
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