To express the solutions to the equation \( x^2 = 18 \) using set notation, we first determine the solutions. The solutions are \( x = -\sqrt{18} \) and \( x = \sqrt{18} \).
Simplifying \( \sqrt{18} \): \[ \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \]
Thus, the solutions are \( -3\sqrt{2} \) and \( 3\sqrt{2} \).
Next, we express these solutions in set notation. Since \( -3\sqrt{2} \) is less than \( 3\sqrt{2} \), we write the set as:
\[ { -3\sqrt{2}, 3\sqrt{2} } \]
Now, for numerical approximation (if needed):
- \( \sqrt{2} \) is approximately \( 1.414 \), thus:
- \( -3\sqrt{2} \approx -4.242 \)
- \( 3\sqrt{2} \approx 4.242 \)
The final answer in set notation is:
\[ { -3\sqrt{2}, 3\sqrt{2} } \]
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