Determine what c-value will create a perfect square trinomial for the following expression: \( x^{2}+14 x+c \)

To create a perfect square trinomial from the expression \( x^{2}+14x+c \), you need to find the right value for \( c \) that makes it a square of a binomial. The formula to do this is \( c = (b/2)^2 \), where \( b \) is the coefficient of \( x \), which in this case is 14. So, \( c = (14/2)^2 = 7^2 = 49 \). Thus, the value of \( c \) that will create a perfect square trinomial is 49. This means the expression will transform into \( (x+7)^2 \), a perfect square trinomial. Perfect square trinomials are not only useful for simplifying expressions, but they also make solving quadratics much easier!