Answer
The real solution set is {-2,-1,0,1}.
Work Step by Step
$|x^2+x-1|=1$
$x^2+x-1=1$ or $x^2+x-1=-1$
$x^2+x-1-1=0$ or $x^2+x+1-1=0$
$x^2+x-2=0$ or $x^2+x=0$
$(x+2)(x-1)=0$ or $x(x+1)=0$
$x+2=0$ or $x-1=0$ or $x =0 $ or $x+1=0$
$x=-2 $ or $x=1$ or $x=0 $ or $x=-1$
The real solution set is {-2,-1,0,1}.