#### Answer

$p=5\text{ or }p=-5$

#### Work Step by Step

We start with the given equation: $p^2+12^2=13^2$
To simplify each of the constants being squared, we multiply them by themselves: $p^2+144=169$
In order to get the term with $p$ by itself, we subtract $144$ from both sides of the equation: $$p^2+144-144=169-144$$$$p^2=25$$
To solve the equation $p^2=25$, we must perform the opposite operation of squaring, which is taking the square root, in order to clear the exponent: $$p^2=25$$$$\sqrt {p^2}=\sqrt {25}$$$$p=\pm5$$$$p=5\text{ or }p=-5$$