Question

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

Answer 1

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.

Answer 2

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}`.