2y^2-1=0

To solve the equation \(2y^2 - 1 = 0\), follow these steps:

1. Isolate the term with \(y^2\): \[ 2y^2 = 1 \]

2. Divide both sides by 2: \[ y^2 = \frac{1}{2} \]

3. Take the square root of both sides: \[ y = \pm \sqrt{\frac{1}{2}} \]

4. Simplify the square root: \[ y = \pm \frac{1}{\sqrt{2}} = \pm \frac{\sqrt{2}}{2} \]

Thus, the solutions to the equation \(2y^2 - 1 = 0\) are: \[ y = \frac{\sqrt{2}}{2} \quad \text{and} \quad y = -\frac{\sqrt{2}}{2} \]