Question

Solve 2x^2+8x-1=0 Using quadratic formula

Answer 1

$\bf \qquad \qquad \textit{quadratic formula}\\\\ \begin{array}{llcclll} &{{ 2}}x^2&{{ +8}}x&{{ +1}}&=0\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \qquad \qquad x= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}$

$\bf x=\cfrac{-8\pm\sqrt{(-8)^2~-~4(2)(1)}}{2(2)}\implies x=\cfrac{-8\pm\sqrt{64~-~8}}{4} \\\\\\ x=\cfrac{-8\pm\sqrt{56}}{4}\implies x=\cfrac{-8\pm\sqrt{4\cdot 14}}{4}\implies x=\cfrac{-8\pm\sqrt{2^2\cdot 14}}{4} \\\\\\ x=\cfrac{-8\pm 2\sqrt{14}}{4}\implies x=\cfrac{-4\pm \sqrt{14}}{2}\implies x= \begin{cases} \cfrac{-4+\sqrt{14}}{2}\\\\ \cfrac{-4 - \sqrt{14}}{2} \end{cases}$