You are given the equation:

\[
A^2 + A^2 = 6
\]

First, simplify the left-hand side:

\[
2A^2 = 6
\]

Now, solve for \( A^2 \) by dividing both sides by 2:

\[
A^2 = \frac{6}{2} = 3
\]

Finally, take the square root of both sides:

\[
A = \pm \sqrt{3}
\]

Thus, \( A = \pm \sqrt{3} \).

Would you like more details or have any questions? 

Here are 5 related questions:
1. What happens if the equation has three \( A^2 \) terms instead of two?
2. How do you solve a cubic equation with similar terms?
3. Can you graph the equation \( A^2 + A^2 = 6 \)?
4. What is the geometric interpretation of this solution in terms of a square's area?
5. How does the square root operation affect the solution set?

**Tip:** Always check for both the positive and negative roots when solving quadratic equations!

Explore how to solve the algebraic equation A^2 + A^2 = 6 and find the value of A. This step-by-step solution covers key algebra concepts such as quadratic equations and square roots, suitable for Grades 8-10.

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