Question

Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 6x + ___?

Answer 1

To create a perfect square trinomial, halve the x coefficient, square it, and then add that value.

In the case of x² + 6x, we would have 6 to get 3, then square 3 to get 9.
We would add 9 to make a perfect square trinomial.

Why this works
A perfect square trinomial is designed to factor to some value (x+n)².
When you FOIL this you get x² + 2nx + n².
As you can see, if you wanted to find the value of that n², you could take that x coefficient 2n, halve it to get n, and then square it to get n²!