From the image, the solution is being attempted for the equation:

$- x^2 + 2 = 0$

Here are the steps for solving this equation:

Step-by-Step Explanation:

1. Start with the given equation: $-x^2 + 2 = 0$

2. Subtract 2 from both sides to isolate the term involving $x^2$: $-x^2 = -2$

3. Divide both sides by $-1$ to make the coefficient of $x^2$ positive: $x^2 = 2$

4. To solve for $x$, take the square root of both sides. Remember, the square root has both positive and negative solutions: $x = \pm \sqrt{2}$

Final Answer:

$x = \sqrt{2} \quad \text{or} \quad x = -\sqrt{2}$

Would you like further clarification or details on this solution?

Here are 5 related questions to expand your understanding:

1. What does it mean when an equation has both positive and negative roots?
2. How can we graph the function $y = -x^2 + 2$ and locate its roots visually?
3. What are the properties of square roots of negative numbers in relation to imaginary numbers?
4. Can this method be used for solving all quadratic equations? If not, why?
5. How does the value $\sqrt{2}$ compare to common square roots like $\sqrt{1}$ or $\sqrt{4}$?

Tip: Always remember to include both positive and negative roots when solving equations like $x^2 = c$.