Case 1: When √x≥2 then |√x−2|=√x−2 ∴ The given equation becomes, ‌(√x−2)+√x(√x−4)+2=0 ⇒(√x−2)+x−4√x+2=0 ⇒x−3√x=0 ⇒√x(√x−3)=0 ∴√x=0 or 3 √x=0 is not possible as √x≥2. So, √x=3 or x=9 Case 2 : When √x<2 then |√x−2|=−(√x−2)=2−√x ∴ The given equation becomes, (2−√x)+√x(√x−4)+2=0 ⇒2−√x+x−4√x+2=0 ⇒x−5√x+4=0 ⇒x−4√x−√x+4=0 ⇒√x(√x−4)−(√x−4)=0 ⇒(√x−4)(√x−1)=0 ∴√x=4 or 1 √x=4 is not possible as √x<2 ∴√x=1 or x=1 So, Sum of all solutions =9+1=10