Answer
$\left\{\dfrac{-5\pm\sqrt{53}}{2}\right\}$
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
x^2+5x=7
,$ is equivalent to
\begin{align*}
x^2+5x-7&=0
.\end{align*}
The equation above has
\begin{align*}a=
1
,b=
5
,\text{ and }c=
-7
.\end{align*}
Using $
x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}
$ or the Quadratic Formula, 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 solution set of $
x^2+5x=7
$ is $
\left\{\dfrac{-5\pm\sqrt{53}}{2}\right\}
$.
