The number of solutions of the equation (3|x|−3)2=|x|+7 which belong to the domain of x(x−3) is

Domain of x(x−3) is x∈(−∞,0]∪[3,∞) Now,  (3|x|−3)2=|x|+7⇒ 9|x|2−19|x|+2=0⇒ (9|x|−1)(|x|−2)=0⇒ |x|=19 or |x|=2⇒ x=−19 or x=−2 Hence, there are 2 solutions to the given equation.