Solving Simple Quadratic Equations Quick Check

Question

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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

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

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

{−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
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Answer 1

To solve the equation \( x^2 = 36169 \) using inspection, we need to find the values of \( x \) that satisfy this equation.

Taking the square root of both sides gives us:

\[ x = \sqrt{36169} \quad \text{or} \quad x = -\sqrt{36169} \]

Calculating \( \sqrt{36169} \):

\[ \sqrt{36169} = 189 \]

Thus, we have two solutions:

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

Therefore, the solution set is:

\[ { -189, 189 } \]

Since this option is not listed as an answer, it seems there may have been a misunderstanding with the values given. The correct solution set for the equation \( x^2 = 36169 \) should be:

\[ {-189, 189} \]

If the options listed don't reflect this, double-check that you have the right context or phrasing provided. However, based on the calculations:

Final correct solution set: {−189, 189}