what are the steps to solve for x

Question

2x^2-1/x^2=0

Answer 1

2 x^2 - 1/x^2 = 0 ???

2 x^4 = 1
x^4 = 1/2

x^2 = (1/2)^.5 or -(1/2)^.5

x = (1/2)^.25 or -(1/2)^.25 or i(1/2)^.25 or -i(1/2)^.25

Answer 2

thank you.i am trying to sove for critical numbers. the book is giving me an answer of

x=+square root 2/2
-

Answer 3

I am wondering if the problem then is this:

(2x^2-1)/x^2=0

2x^2=1
x= +- sqrt (1/2)

but of course, multiplying that by sqrt(2/2) one gets
x= +- sqrt (2/4)= +- .5 sqrt 2