Answer
$x=\dfrac{2-i\sqrt{10}}{2}
\text{ OR }
x=\dfrac{2+i\sqrt{10}}{2}$
Work Step by Step
In the given equation,
\begin{align*}
2x^2-4x+7=0
,\end{align*} $a=
2
,$ $b=
-4
,$ and $c=
7
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(7)}}{2(2)}
\\\\&=
\dfrac{4\pm\sqrt{16-56}}{4}
\\\\&=
\dfrac{4\pm\sqrt{-40}}{4}
\\\\&=
\dfrac{4\pm\sqrt{-1}\cdot\sqrt{4}\cdot\sqrt{10}}{4}
\\\\&=
\dfrac{4\pm\sqrt{-1}\cdot2\cdot\sqrt{10}}{4}
\\\\&=
\dfrac{4\pm i\cdot2\cdot\sqrt{10}}{4}
&\text{ (use $i=\sqrt{-1}$)}
\\\\&=
\dfrac{4\pm 2i\sqrt{10}}{4}
\\\\&=
\dfrac{\cancel4^2\pm \cancel2^1i\sqrt{10}}{\cancel4^2}
&\text{ (divide by $2$)}
\\\\&=
\dfrac{2\pm i\sqrt{10}}{2}
.\end{align*}
The solutions are $
x=\dfrac{2-i\sqrt{10}}{2}
\text{ and }
x=\dfrac{2+i\sqrt{10}}{2}
.$
