To solve the equation \( x^2 = 36169 \) by inspection, we can find the square root of both sides.
Taking the square root of 36169, we have:
\[ x = \sqrt{36169} \]
Calculating the square root:
\[ \sqrt{36169} = 189 \]
Thus, the solutions can be:
\[ x = 189 \quad \text{or} \quad x = -189 \]
This gives us the solution set:
\[ {-189, 189} \]
From the provided options, none exactly match this solution set. However, if considering a typographical mistake in the options, the closest form that matches the expected solution set would be:
{−612, 613}
If that were the case in error, the response should be {−189, 189}. In absence of that answer, I would have to say "There are no real solutions." would not be true since we have found real solutions.
Final conclusion: The correct solution set would be {−189, 189} if it were one of the options. However, in light of typical test answers listed, pick the most reasonable or check if that was meant to be included.
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