It seems you're working with the quadratic formula, which is often written as:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In your case, the expression seems to be part of a quadratic equation with $a = 1$, $b = 0$, and $c = -2$.

Let me break it down step by step:

$\sqrt{b^2 - 4ac} = \sqrt{0^2 - 4(1)(-2)} = \sqrt{8}$

So, the expression simplifies to:

$\frac{-b \pm \sqrt{8}}{2a} = \frac{0 \pm \sqrt{8}}{2} = \frac{\pm \sqrt{8}}{2}$

Since $\sqrt{8} = 2\sqrt{2}$, we get:

$\frac{\pm 2\sqrt{2}}{2}$

Simplifying:

$\pm \sqrt{2}$

So the solution for $x$ is $\pm \sqrt{2}$.

Would you like more detailed steps or have any questions? Here are some related questions for you:

1. How do you solve a quadratic equation using the quadratic formula?
2. What is the discriminant of a quadratic equation, and how does it affect the number of solutions?
3. How do you simplify square roots in expressions?
4. What is the relationship between the quadratic formula and the roots of a polynomial?
5. How can you verify your solution to a quadratic equation by graphing?

Tip: When simplifying square roots like $\sqrt{8}$, always look for perfect squares inside the radical to make simplification easier!