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