To solve the equation [tex]\(x^2 + 4 = 0\)[/tex], we will follow a systematic approach:
1. Rewrite the equation:
[tex]\[
x^2 + 4 = 0
\][/tex]
2. Isolate the [tex]\(x^2\)[/tex] term:
[tex]\[
x^2 = -4
\][/tex]
3. Recognize that we need to take the square root of both sides.
4. Take the square root of both sides:
[tex]\[
x = \pm \sqrt{-4}
\][/tex]
5. Simplify the square root of [tex]\(-4\)[/tex]:
[tex]\[
\sqrt{-4} = \sqrt{4 \cdot (-1)} = \sqrt{4} \cdot \sqrt{-1}
\][/tex]
Knowing that [tex]\(\sqrt{4} = 2\)[/tex] and [tex]\(\sqrt{-1} = i\)[/tex]:
[tex]\[
\sqrt{-4} = 2i
\][/tex]
Thus, the solutions to the equation [tex]\(x^2 + 4 = 0\)[/tex] are:
[tex]\[
x = \pm 2i
\][/tex]
So, the correct answer is:
[tex]\[ x = \pm 2i \][/tex]
