To find the solutions to the equation [tex]\( x^2 - 1 = 399 \)[/tex], we can follow these steps:
1. Rewrite the equation:
[tex]\[
x^2 - 1 = 399
\][/tex]
2. Isolate the quadratic term:
Add 1 to both sides:
[tex]\[
x^2 - 1 + 1 = 399 + 1
\][/tex]
Simplifies to:
[tex]\[
x^2 = 400
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Take the square root of both sides:
[tex]\[
x = \pm \sqrt{400}
\][/tex]
Simplifies to:
[tex]\[
x = \pm 20
\][/tex]
Therefore, the solutions to the equation [tex]\( x^2 - 1 = 399 \)[/tex] are [tex]\( x = 20 \)[/tex] and [tex]\( x = -20 \)[/tex].
Thus, the correct answer is:
A. [tex]\( x = 20 \)[/tex] and [tex]\( z = -20 \)[/tex]
