Question

Solutions of the equation $x|x+1|+1=0$ are

Answer 1

$x|x+1|+1=0$

if $x>-1$

$x(x+1)+1=0$

$\Rightarrow$$x^2+x+1=0$

$x=\frac{-1\pm \sqrt{1-4}}{2}$

$=\frac{-1\pm \sqrt{-3}}{2}$

$=\frac{-1\pm i\sqrt{3}}{2}$

if $x<-1$

$-x(x+1)+1=0$

$\Rightarrow$$x^2+x-1=0$

$x=\frac{-1\pm \sqrt{5}}{2}$

$=\frac{1}{2}(-1\pm \sqrt{5})$