If x raise to power two +14x +k is a perfect square find k

Answer 1

x^2 + 14x + k
= x^2 + 14x + 49 + k - 49
= (x+7)^2 + k-49
if (x+7)^2 = x^2 + 14x + k , k-49 = 0 or k = 49

or
(x + a)^2 = x^2 + 2ax + a^2
compare with x^2 + 14x + k, then
2ax = 14x
2a = 14
a = 7 and k = a^2 = 49

or, by just knowing the result of (a + b)^2
x^2 + 14x + k, take half of 14, then square it.