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The equation provided is:

\[
10 - 3a^2 = -2
\]

### To solve for \(a\):

1. Subtract 10 from both sides:

\[
-3a^2 = -2 - 10
\]

\[
-3a^2 = -12
\]

2. Divide both sides by \(-3\):

\[
a^2 = \frac{-12}{-3}
\]

\[
a^2 = 4
\]

3. Take the square root of both sides:

\[
a = \pm \sqrt{4}
\]

\[
a = \pm 2
\]

### Solution:
The values of \(a\) are \(a = 2\) and \(a = -2\).

Would you like more details or clarifications on this solution?

Here are 5 related questions to further your understanding:

1. What happens if the right-hand side of the equation were positive instead of negative?
2. How would you solve the equation if it were \(10 - 3a^2 = 0\)?
3. Can you solve similar quadratic equations using the quadratic formula?
4. What does it mean to have two solutions for \(a\)? How does this relate to the graph of the equation?
5. What if the coefficient of \(a^2\) was different, like \(10 - 5a^2 = -2\)?

**Tip**: Always check both positive and negative roots when solving for a variable squared!

Discover how to solve the quadratic equation 10 - 3a^2 = -2 through a step-by-step guide. This solution includes key algebraic concepts, such as solving for variables and taking square roots. Perfect for students in Grades 7-9.

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