## Intermediate Algebra (6th Edition)

$x=\left\{ \dfrac{2}{5},-\dfrac{1}{2} \right\}$
Multiplying both sides by the $LCD= 20$, then the solution to the given equation, $\dfrac{x^2}{2}+\dfrac{x}{20}=\dfrac{1}{10}$, is \begin{array}{} 10(x^2)+1(x)=2(1) \\\\ 10x^2+x=2 \\\\ 10x^2+x-2=0 \\\\ (5x-2)(2x+1)=0 .\end{array} Equating each factor to zero, then $x=\left\{ \dfrac{2}{5},-\dfrac{1}{2} \right\}$.