Answer
$\{ -12, 1 \}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
p^2+11p-12=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(11)\pm\sqrt{(11)^2-4(1)(-12)}}{2(1)}
\\\\=
\dfrac{-11\pm\sqrt{121+48}}{2}
\\\\=
\dfrac{-11\pm\sqrt{169}}{2}
\\\\=
\dfrac{-11\pm\sqrt{(13)^2}}{2}
\\\\=
\dfrac{-11\pm13}{2}
\\\\=
\dfrac{-11-13}{2}
\text{ OR }
\dfrac{-11+13}{2}
\\\\=
\dfrac{-24}{2}
\text{ OR }
\dfrac{2}{2}
\\\\=
-12
\text{ OR }
1
.\end{array}
Hence, the solutions are $
\{ -12, 1 \}
.$
