Is this reasoning for finding the solutions of the equation  correct?  is given: 2x2 –1 =...

Is this reasoning for finding the solutions of the equation  correct?  is given: 2x2 –1 = x 2, obtained by squaring both sides of (1); x2–1 = 0, obtained by subtracting x2 from both sides of (2); (4) (x –1)( x +1)= 0, obtained by factoring the left-hand side of x2– 1; (5) x = 1 or x= -1. which follows because ab =0 implies that a = 0 or b = 0.