Use inspection to solve the equation x2=36169, then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)

Question

Responses

{−613,613}
left brace negative Start Fraction 6 over 13 End Fraction comma Start Fraction 6 over 13 End Fraction right brace

{−613}
left brace negative Start Fraction 6 over 13 End Fraction right brace

{613}
left brace Start Fraction 6 over 13 End Fraction right brace

There are no real solutions.

Answer 1

To solve the equation \( x^2 = 36169 \) by inspection, we can take the square root of both sides.

Taking the square root gives us:

\[ x = \pm \sqrt{36169} \]

Calculating the square root:

\[ \sqrt{36169} = 189 \]

Therefore, the solutions are:

\[ x = 189 \quad \text{and} \quad x = -189 \]

Thus, the solution set is:

\[ {-189, 189} \]

Since the options presented do not list {-189, 189}, let's check for any potential typographical issues in your options. However, since 189 can also be expressed with a sign, the closest approach based on normal notation and assuming no typographical error is required in decimal form.

None of the provided options accurately represent this set. If we follow the most logical answer based on the computation \( { -189, 189 } \), but if that's not listed, it may likely be that this particular form may not be represented well.

Based on the computation done above, the solutions should be expressed correctly as \( {-189, 189} \).

Given that none of the choices reflect upon correctly, consult either from the provided set depending upon the new assessment of numbers, or raise a note about the potential misfit in the answer choices listed.