To solve the equation [tex]\( x^2 - 25 = 0 \)[/tex], let's follow these steps:
1. Start with the given equation:
[tex]\[
x^2 - 25 = 0
\][/tex]
2. Move the constant term to the right side of the equation to isolate the [tex]\( x^2 \)[/tex] term:
[tex]\[
x^2 = 25
\][/tex]
3. Take the square root of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \sqrt{25} \quad \text{or} \quad x = -\sqrt{25}
\][/tex]
4. Simplify the square roots:
[tex]\[
\sqrt{25} = 5 \quad \text{and} \quad -\sqrt{25} = -5
\][/tex]
So, we end up with two solutions:
[tex]\[
x = 5 \quad \text{and} \quad x = -5
\][/tex]
Therefore, the correct answer is:
[tex]\[
\text{D. } x = 5 ; x = -5
\][/tex]
