To solve the equation \( X^2 = \frac{49}{169} \), we will take the square root of both sides.

\[
X = \pm \sqrt{\frac{49}{169}}
\]

This can be broken down as:

\[
X = \pm \frac{\sqrt{49}}{\sqrt{169}}
\]

Since \(\sqrt{49} = 7\) and \(\sqrt{169} = 13\), we have:

\[
X = \pm \frac{7}{13}
\]

So, the solution is:

\[
X = \frac{7}{13} \quad \text{or} \quad X = -\frac{7}{13}
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What is the general method for solving quadratic equations?
2. How do you solve a quadratic equation by factoring?
3. What is the significance of the discriminant in quadratic equations?
4. How can you graph the solutions to a quadratic equation?
5. What are the applications of quadratic equations in real-life situations?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the equation X² = 49/169 step-by-step with detailed explanations. This problem involves algebraic concepts such as quadratic equations, square roots, and fraction operations. Suitable for students in Grades 7-9.

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