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Question:

$8 x^{2}+2 x+1=0$

 

Solution:

Given:

$8 x^{2}+2 x+1=0$

Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:

$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$

$\Rightarrow x=\frac{-2 \pm \sqrt{(2)^{2}-(4 \times 8 \times 1)}}{2 \times 8}$

$\Rightarrow x=\frac{-2 \pm \sqrt{4-32}}{16}$

$\Rightarrow x=\frac{-2 \pm \sqrt{-28}}{16}$

$\Rightarrow x=\frac{-2 \pm 2 \sqrt{7} i}{16}$

$\Rightarrow x=-\frac{2}{16} \pm \frac{2 \sqrt{7}}{16} i$

Ans: $x=-\frac{1}{8}+\frac{\sqrt{7}}{8} i$ and $x=-\frac{1}{8}-\frac{\sqrt{7}}{8} i$

 

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