The given equation is:

\[ x^2 + 2y = 0 \]

To solve this equation for \( y \) in terms of \( x \), follow these steps:

1. **Isolate \( y \)**:
   \[
   2y = -x^2
   \]

2. **Divide by 2** to solve for \( y \):
   \[
   y = -\frac{x^2}{2}
   \]

So, the equation solved for \( y \) in terms of \( x \) is:

\[
y = -\frac{x^2}{2}
\]

This equation represents a downward-opening parabola that has been scaled by a factor of \(\frac{1}{2}\).

Would you like more details or have any questions about this? Here are some related questions you might find helpful:

1. What are the key properties of a parabola?
2. How do you find the vertex of the parabola \( y = -\frac{x^2}{2} \)?
3. How can you graph the equation \( y = -\frac{x^2}{2} \)?
4. What is the axis of symmetry for this parabola?
5. How does changing the coefficient of \( x^2 \) affect the shape of a parabola?

**Tip:** Remember, the sign in front of the \( x^2 \) term determines whether a parabola opens upwards or downwards.

Learn how to solve the equation x^2 + 2y = 0 to find y in terms of x with a step-by-step solution. This problem involves algebraic manipulation, focusing on isolating variables and understanding parabolic equations. Suitable for high school students and above.

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