Verified answer

[tex]2 {x}^{2} - 1 = 0 \\ {x}^{2} - \frac{1}{2} = 0 \\ (x - \frac{1}{ \sqrt{2} } )(x + \frac{ 1 }{ \sqrt{2} } ) = 0 \\ (x - \frac{ \sqrt{2} }{2} )(x + \frac{ \sqrt{2} }{2} ) = 0 \\ x_{1} = \frac{ \sqrt{2} }{2} \\ x _{2} = - \frac{ \sqrt{2} }{2} [/tex]