Question
Both -6 and 6 make the equation x to the 2 power/2 = 18 true. Use set notation to express these solutions. When entering your response, list elements in the set from least to greatest, with a comma between each element in the set. (Remember to include all the values that make the equation true within the set. List the elements of the set from least to greatest, with a comma between each element in the set)
Answers
GPT-4o mini
To express the solutions of the equation \(\frac{x^2}{2} = 18\) in set notation, we first solve for \(x\).
1. Multiply both sides of the equation by 2:
\[
x^2 = 36
\]
2. Take the square root of both sides:
\[
x = 6 \quad \text{or} \quad x = -6
\]
The solutions are \(6\) and \(-6\). In set notation, we can express these solutions as:
\[
\{-6, 6\}
\]
So the final expression in set notation is:
\(\{-6, 6\}\)
1. Multiply both sides of the equation by 2:
\[
x^2 = 36
\]
2. Take the square root of both sides:
\[
x = 6 \quad \text{or} \quad x = -6
\]
The solutions are \(6\) and \(-6\). In set notation, we can express these solutions as:
\[
\{-6, 6\}
\]
So the final expression in set notation is:
\(\{-6, 6\}\)