Question

what is the value of c such that: x^2+14x+c is a perfect-square trinomial?

Answer 1

We are asked to find a value of $c$  in which the trinomial $x^2+14x+c$ is a perfect square trinomial. The easiest way to do this is by using a method called completing the square. This method calls for taking half of the $b$ term and squaring it. In this case, the $b$ term is 14. When we halve it, we get $14 / 2 = 7$. When we square it, we get $7^2=49$. Therefore, the value of $c$ in the trinomial $x^2+14x+c$ is $\boxed{49}$. 

Answer 2

That value of c would be 49.  To obtain this, take the coefficient (14) of the x term, halve it, and then square the result:  half of 14 is 7, and the square of 7 is 49.