Question

+Find the number to add to x2 + 14x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.O add 49; (x + 7)?o add 196; (x + 14)2o add 28: (x + 14)2O add 14; (x + 7)?

Answer 1

A binomial square have the following form:

$(x+a)^2=x^2+2ax+a^2$

So, from the coefficient of the second term, we can get the value a and with the value a we can calculate a² for the value of the third term, that is, the value we need to add to make it a perfect square.

We have the expression:

$x^2+14x$

By comparing the second terms, we see that:

$\begin{gathered} 14=2a \\ 2a=14 \\ a=\frac{14}{2} \\ a=7 \end{gathered}$

Since we have a, we can calculate a²:

$a^2=7^2=49$

So, this means the number we need to add is 49 and, since a is 7, the trinomial can be rewritten as:

$x^2+14x+49=(x+7)^2$

So, add 49 and the square binomial is:

$(x+7)^2$