To solve the equation [tex]\(x^2 - 4 = 0\)[/tex], we need to find the values of [tex]\(x\)[/tex] that make the equation true. Let's go through this step-by-step:
1. Start with the given equation:
[tex]\[
x^2 - 4 = 0
\][/tex]
2. Rewrite the equation by adding 4 to both sides:
[tex]\[
x^2 - 4 + 4 = 0 + 4
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 = 4
\][/tex]
3. To solve for [tex]\(x\)[/tex], we need to take the square root of both sides. Remember that the square root of 4 has two solutions: one positive and one negative. Thus:
[tex]\[
x = \sqrt{4} \quad \text{or} \quad x = -\sqrt{4}
\][/tex]
4. Simplify the square roots:
[tex]\[
x = 2 \quad \text{or} \quad x = -2
\][/tex]
Therefore, the solutions to the equation [tex]\(x^2 - 4 = 0\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -2\)[/tex].
The correct answer is:
[tex]\[
x = -2 \text{ or } x = 2
\][/tex]
