import math

# Simplify the square root of 61
simplified_sqrt_61 = math.sqrt(61)

# Calculate the two possible values for x
x1 = 6 + simplified_sqrt_61
x2 = 6 - simplified_sqrt_61

simplified_sqrt_61, x1, x2The square root of 61 simplifies to approximately \( \sqrt{61} \approx 7.81 \).

Thus, the two possible values for \( x \) are:

1. \( x \approx 6 + 7.81 = 13.81 \)
2. \( x \approx 6 - 7.81 = -1.81 \)

Since \( x \) represents an angle in degrees, the negative value \( x \approx -1.81 \) is not physically meaningful in this context. Therefore, the valid solution is:

\[
x \approx 13.81^\circ
\]

Do you need any further explanation on this? 

### Related Questions:
1. What are other methods for simplifying square roots?
2. How can you approximate square roots without a calculator?
3. Why do we discard negative solutions in geometry?
4. Can all quadratic equations be solved exactly?
5. What is the importance of checking your work in algebra?

### Tip:
Always verify the context of your problem to ensure that the solutions you keep are meaningful and applicable.

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