# The solution set of the equation $|x^2+x|=x^2+x$ is

(A) $(-\infty,-1]$

(B) $(0,\infty]$

(C) $[-1,0]$

(D) $(-\infty,-1]\cup [0,\infty)$

Given: $|x^2+x|=x^2+x$
Since modulus of a number is positive,
$x^2+x\geq 0$
$\Rightarrow\:x(x+1)\geq 0$
$\Rightarrow\:x\geq 0\:\:or\:x\leq -1$
$x\in (-\infty,-1]\cup [0,\infty)$