To solve the equation [tex]\(x^2 - 1 = 399\)[/tex], we need to follow these steps:
1. Isolate the quadratic term: Start by adding 1 to both sides of the equation to isolate [tex]\(x^2\)[/tex].
[tex]\[
x^2 - 1 + 1 = 399 + 1
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 = 400
\][/tex]
2. Solve for [tex]\(x\)[/tex]: Take the square root of both sides of the equation to solve for [tex]\(x\)[/tex]. It is important to remember that when you take the square root of both sides, you must consider both the positive and negative roots.
[tex]\[
x = \pm \sqrt{400}
\][/tex]
3. Calculate the square roots: Determine the value of [tex]\(\sqrt{400}\)[/tex].
[tex]\[
\sqrt{400} = 20
\][/tex]
Therefore, the solutions are:
[tex]\[
x = 20 \quad \text{and} \quad x = -20
\][/tex]
As a result, the solutions to the equation [tex]\(x^2 - 1 = 399\)[/tex] are:
[tex]\[
\boxed{x = 20 \text{ and } x = -20}
\][/tex]
The correct answer is:
A. [tex]\(x=20\)[/tex] and [tex]\(x=-20\)[/tex]
