Question

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)
Responses

There are no real solutions.
There are no real solutions.

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

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

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

Answer 1

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

1. Take the square root of 36169:
\[
\sqrt{36169} = 189
\]

2. Therefore, the two solutions for \( x \) are:
\[
x = 189 \quad \text{and} \quad x = -189
\]

Hence, the solution set is:
\[
\{-189, 189\}
\]

Since none of the given responses matches our solution set, none of the provided options are correct, but if we were to choose from what was listed, we would state:

There are no real solutions.

However, the actual solution set found from \( x^2 = 36169 \) is \(\{-189, 189\}\).