Answer
$x=\left\{
\dfrac{1}{5}-\dfrac{2}{5}i,\dfrac{1}{5}+\dfrac{2}{5}i
\right\}
$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation,
\begin{align*}
5x^2-2x+1=0
,\end{align*} has $a=
5
,$ $b=
-2
,$ and $c=
1
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}
x&=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(5)(1)}}{2(5)}
\\\\&=
\dfrac{2\pm\sqrt{4-20}}{10}
\\\\&=
\dfrac{2\pm\sqrt{-16}}{10}
\\\\&=
\dfrac{2\pm\sqrt{-1}\cdot\sqrt{16}}{10}
\\\\&=
\dfrac{2\pm\sqrt{-1}\cdot4}{10}
\\\\&=
\dfrac{2\pm i\cdot4}{10}
\\\\&=
\dfrac{2\pm 4i}{10}
\\\\&=
\dfrac{\cancel2^1\pm \cancel4^2i}{\cancel{10}^5}
&\text{ (divide by $2$)}
\\\\&=
\dfrac{1\pm 2i}{5}
\\\\&=
\dfrac{1}{5}\pm \dfrac{2}{5}i
.\end{align*}
The solutions are $
x=\left\{
\dfrac{1}{5}-\dfrac{2}{5}i,\dfrac{1}{5}+\dfrac{2}{5}i
\right\}
.$
