Answer
number to be added: $49$
factored form: $(p+7)^2$
Work Step by Step
RECALL:
To complete the square for an expression in the form $x^2+bx$, $(\frac{b}{a})^2$ must be added.
The factored form of the result is $(x+\frac{b}{2})^2$.
Thus, in the given expression add $(\frac{14}{2})^2=7^2=49$ to obtain:
$p^2 + 14p + 49$
Writing the square in factored form gives:
$p^2+14p+49 = (p+7)^2$
