Are You Good With Modulus?

Equation: $x^2+x-|x|-4=0$

CASE I: If $x\geq0$ , then equation becomes $x^2+x-x-4=0$

$\Rightarrow$ $x=\pm2$

So, $x=2$ is a solution in this case.

CASE II: If $x<0$ , then equation becomes $x^2+x-(-x)-4=0$

$\Rightarrow$ $x^2+2x-4=0$

$\Rightarrow$ $x=-1\pm\sqrt{5}$

So, $x=-1-\sqrt{5}$ is a solution in this case.

Therefore, $Sum=2-1-\sqrt{5}$

$\Rightarrow$ $1-\sqrt{5}$

$\Rightarrow$ $a+b=1+5=6$ $\ddot\smile$