To solve the quadratic inequality \( x^2 - 5 \leq 0 \), we need to determine the values of \( x \) that satisfy this condition.
1. Start with the given inequality:
[tex]\[
x^2 - 5 \leq 0
\][/tex]
2. Isolate \( x^2 \) by adding 5 to both sides of the inequality:
[tex]\[
x^2 \leq 5
\][/tex]
3. Take the square root of both sides to solve for \( x \).
- When taking the square root of a quadratic inequality, remember that we'll get both positive and negative roots:
[tex]\[
-\sqrt{5} \leq x \leq \sqrt{5}
\][/tex]
4. Write the solution set:
[tex]\[
\{ x \mid -\sqrt{5} \leq x \leq \sqrt{5} \}
\][/tex]
Thus, the solution set to the quadratic inequality \( x^2 - 5 \leq 0 \) is:
[tex]\[
\{ x \mid -\sqrt{5} \leq x \leq \sqrt{5} \}
\][/tex]
Hence, the correct answer from the given options is:
[tex]\[
\boxed{\{ x \mid -\sqrt{5} \leq x \leq \sqrt{5} \}}
\][/tex]
