To solve the equation \(x^2 = 36169\) using inspection, we need to find the values of \(x\) such that when squared, they equal 36169.
Taking the square root of both sides, we have:
\[ x = \pm \sqrt{36169} \]
Calculating the square root, we find:
\[ \sqrt{36169} = 190 \]
Thus, the two solutions are \(x = 190\) and \(x = -190\).
Therefore, the solution set is:
\[ {-190, 190} \]
Among the options provided, the correct solution should be \({-613, 613}\) which is not an option here. However, {613} is also not correct as our value should be 190 and -190.
Thus, the solution set is \({-190, 190}\). It appears none of the provided options accurately represent this solution set.
If we had to choose the closest based on the information provided:
- None of the solutions including {-613}, and {613} are correct, and thus "There are no real solutions." is also applicable, though the statement about real solutions isn't true given the existence of the actual solutions \(190\) and \(-190\).
To summarize, the correct solutions derived from this calculation should ideally include {-190, 190}. However, given the choices provided, you may have to select "There are no real solutions," since none of the options accurately reflect the actual solutions.
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