Explanation:

Given equation is |x−3|² +|x−3|−2=0,
To solve this equation consider |x−3|=a,
a²+a−2=0
= (a+2)(a−1)=0
= a=−2 or a=1,
But |x−3| cannot be a negitive number,
= |x−3|=1
= x−3=±1
= x=4,2,
∴ sum of all the real roots is 4+2=6