Question

What is the solution set of the quadratic equation 8x2 +2x +1 =0?

Answer 1

   
$\displaystyle\\ 8x^2 +2x +1 =0\\\\ x_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-2\pm \sqrt{2^2-4\cdot 8 \cdot 1}}{2\cdot 8}=\\\\ =\frac{-2\pm \sqrt{4-32}}{16}=\frac{-2\pm \sqrt{-28}}{16}=\frac{-2\pm \sqrt{4\cdot 7\cdot(-1)}}{16}=\\\\ =\frac{-2\pm 2i\sqrt{7}}{16}=\frac{-1\pm i\sqrt{7}}{8}= -\frac{1}{8}\pm \frac{\sqrt{7}}{8}i\\\\ x_1 = \boxed{-\frac{1}{8}+ \frac{\sqrt{7}}{8}i}\\\\ x_2 = \boxed{-\frac{1}{8}- \frac{\sqrt{7}}{8}i}\\\\ x_1,~x_2~\in \mathbb{C}$