Sure, let's solve the equation [tex]\(x^2 + 25 = 0\)[/tex] by taking square roots step-by-step.
1. Start with the given equation:
[tex]\[
x^2 + 25 = 0
\][/tex]
2. Subtract 25 from both sides to isolate [tex]\(x^2\)[/tex]:
[tex]\[
x^2 = -25
\][/tex]
3. To solve for [tex]\(x\)[/tex], take the square root of both sides. Remember that the square root of a negative number involves an imaginary unit [tex]\(i\)[/tex], where [tex]\(i\)[/tex] is defined as [tex]\(\sqrt{-1}\)[/tex]:
[tex]\[
x = \pm \sqrt{-25}
\][/tex]
4. Rewrite [tex]\(\sqrt{-25}\)[/tex] using imaginary numbers:
[tex]\[
\sqrt{-25} = \sqrt{25 \cdot (-1)} = \sqrt{25} \cdot \sqrt{-1} = 5i
\][/tex]
5. Therefore, the solutions are:
[tex]\[
x = \pm 5i
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\pm 5i}
\][/tex]
Therefore, the correct option is d. [tex]\(\pm 5i\)[/tex].
