Answer
$x=\left\{
\dfrac{5-\sqrt{53}}{2},\dfrac{5+\sqrt{53}}{2}
\right\}
$
Work Step by Step
In the given equation,
\begin{align*}
x^2-5x-7=0
,\end{align*} $a=
1
,$ $b=
-5
,$ and $c=
-7
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}x&=
\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(-7)}}{2(1)}
\\\\&=
\dfrac{5\pm\sqrt{25+28}}{2}
\\\\&=
\dfrac{5\pm\sqrt{53}}{2}
.\end{align*}
Hence, the solutions are $
x=\left\{
\dfrac{5-\sqrt{53}}{2},\dfrac{5+\sqrt{53}}{2}
\right\}
.$
