Question

Solve the following quadric equations by factorization method only $x^2+x+1=0$

Answer 1

$x^2+x+1=0\text{Now, completing the squares, we get}{(x+\frac{1}{2})}^2+\frac{3}{4}=0\Rightarrow {(x+\frac{1}{2})}^2-{\left(\frac{\sqrt{3}}{2}i\right)}^2=0\Rightarrow (x+\frac{1}{2}+\frac{\sqrt{3}}{2}i)(x+\frac{1}{2}-\frac{\sqrt{3}}{2}i)=0\Rightarrow (x+\frac{1}{2}+\frac{\sqrt{3}}{2}i)=0Or(x+\frac{1}{2}-\frac{\sqrt{3}}{2}i)=0\therefore x=\frac{-1}{2}+\frac{\sqrt{3}}{2}i,\frac{-1}{2}-\frac{\sqrt{3}}{2}i$