Answer:
[tex]\text{C. }\pm \frac{1}{2}[/tex]
Step-by-step explanation:
Start by moving the 2 to the right (so we can multiply both sides by the denominator):
[tex]\frac{1}{2x^2-1}=-2[/tex]
Multiply both sides by [tex]2x^2-1[/tex]:
[tex]1=-2(2x^2-1),\\1=-4x^2+2[/tex]
Move everything to one side:
[tex]4x^2-2+1=0,\\4x^2-1=0,\\4x^2=1,\\x^2=\frac{1}{4},\\x=\boxed{\pm\frac{1}{2}}[/tex]
