Question

x² + 2x + 5 = 0

Answer 1

Given: $x^2+2x+5=0$

$$\begin{gathered} x^2+2x+5=0 \\ \Rightarrow x^2+2x+1+4=0 \\ \Rightarrow (x+1{)}^2-(2i{)}^2=0\left[\right(a+b{)}^2=a^2+b^2+2ab] \\ \Rightarrow (x+1+2i)(x+1-2i)=0[a^2-b^2=(a+b)(a-b)] \end{gathered}$$
$\Rightarrow (x+1+2i)=0$ or, $(x+1-2i)=0$
$\Rightarrow x=-(1+2i)$ or, $x=-1+2i$
Hence, the roots of the equation are $-1+2i\mathrm{and}-1-2i$.