To solve the equation \( x^2 = 18 \), we can take the square root of both sides. This gives us:
\[
x = \sqrt{18} \quad \text{or} \quad x = -\sqrt{18}
\]
Since \( \sqrt{18} = 3\sqrt{2} \), we can express the two solutions as:
\[
x = 3\sqrt{2} \quad \text{and} \quad x = -3\sqrt{2}
\]
The approximate numerical values of these solutions are \( 3\sqrt{2} \approx 4.24 \) and \( -3\sqrt{2} \approx -4.24 \).
However, you mentioned that both \(-6\) and \(6\) make the equation true. Let's verify:
Substituting \(x = 6\):
\[
6^2 = 36 \quad \text{(not true for } x^2 = 18 \text{)}
\]
Substituting \(x = -6\):
\[
(-6)^2 = 36 \quad \text{(also not true for } x^2 = 18 \text{)}
\]
So it appears there might be a misunderstanding about the solutions to the equation based on your prompt.
The actual solutions for \(x^2 = 18\) are:
\[
{-3\sqrt{2}, 3\sqrt{2}}
\]
In numeric terms, approximating \(3\sqrt{2} \approx 4.24\) and \( -3\sqrt{2} \approx -4.24\), we present the solutions in increasing order. The final answer for the solutions in set notation is:
\[
{-3\sqrt{2}, 3\sqrt{2}}
\]
If we want to list them in decimal approximations from least to greatest, we would represent it as:
\[
{-4.24, 4.24}
\]
However, since you initially mentioned \(-6\) and \(6\) (which do not satisfy \(x^2 = 18\)), if you're still interested in writing those numbers in set notation, the correct context is:
\[
{-6, 6}
\]
Just be aware that these do not satisfy the original equation \(x^2 = 18\).