To solve the equation [tex]\(x^2 - 1 = 399\)[/tex], follow these steps:
1. Rewrite the Equation: First, we need to isolate the [tex]\(x^2\)[/tex] term. To do this, add 1 to both sides of the equation:
[tex]\[
x^2 - 1 + 1 = 399 + 1
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 = 400
\][/tex]
2. Solve for [tex]\(x\)[/tex]: The next step is to solve for [tex]\(x\)[/tex]. We take the square root of both sides of the equation:
[tex]\[
x = \pm \sqrt{400}
\][/tex]
3. Calculate the Square Root: Calculate the square root of 400:
[tex]\[
\sqrt{400} = 20
\][/tex]
Therefore,
[tex]\[
x = \pm 20
\][/tex]
This means [tex]\(x\)[/tex] can either be positive 20 or negative 20.
So, the solutions to the equation [tex]\(x^2 - 1 = 399\)[/tex] are:
[tex]\[
x = 20 \quad \text{and} \quad x = -20
\][/tex]
Hence, the correct answer is:
A. [tex]\(x = 20\)[/tex] and [tex]\(x = -20\)[/tex].
