Solve this

Question:

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

 

Solution:

Given:

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

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

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

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

$\Rightarrow x=\frac{-2 \pm \sqrt{4-8}}{2}$

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

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

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

$\Rightarrow^{x}=-1 \pm i$

Ans: $x=-1+i$ and $x=-1-i$

 

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