To solve for [tex]\( P \)[/tex] in the equation [tex]\( P^2 - 8 = 17 \)[/tex], we can follow these steps:
1. Rewrite the equation: Start by manipulating the given equation to isolate the term containing [tex]\( P \)[/tex]. Given the equation:
[tex]\[
P^2 - 8 = 17
\][/tex]
2. Add 8 to both sides: To isolate [tex]\( P^2 \)[/tex], add 8 to both sides of the equation:
[tex]\[
P^2 - 8 + 8 = 17 + 8
\][/tex]
Simplifying this, we get:
[tex]\[
P^2 = 25
\][/tex]
3. Solve for [tex]\( P \)[/tex]: To find [tex]\( P \)[/tex], we take the square root of both sides of the equation. Remember that squaring a number always gives a non-negative result, so we need to consider both the positive and negative roots:
[tex]\[
P = \pm \sqrt{25}
\][/tex]
Since the square root of 25 is 5, we have:
[tex]\[
P = \pm 5
\][/tex]
Thus, the possible values of [tex]\( P \)[/tex] are [tex]\( P = 5 \)[/tex] and [tex]\( P = -5 \)[/tex]. Therefore, the following are possible values of [tex]\( P \)[/tex]:
[tex]\[
\boxed{5 \text{ and } -5}
\][/tex]
