[tex]\bf \qquad \qquad \textit{quadratic formula}\\\\
\begin{array}{llcclll}
&{{ 2}}x^2&{{ +8}}x&{{ +1}}&=0\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad \qquad
x= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}[/tex]
[tex]\bf x=\cfrac{-8\pm\sqrt{(-8)^2~-~4(2)(1)}}{2(2)}\implies x=\cfrac{-8\pm\sqrt{64~-~8}}{4}
\\\\\\
x=\cfrac{-8\pm\sqrt{56}}{4}\implies x=\cfrac{-8\pm\sqrt{4\cdot 14}}{4}\implies x=\cfrac{-8\pm\sqrt{2^2\cdot 14}}{4}
\\\\\\
x=\cfrac{-8\pm 2\sqrt{14}}{4}\implies x=\cfrac{-4\pm \sqrt{14}}{2}\implies x=
\begin{cases}
\cfrac{-4+\sqrt{14}}{2}\\\\
\cfrac{-4 - \sqrt{14}}{2}
\end{cases}[/tex]
