For this case we have the following trinomial:
\(x ^ 2 + 7x + c
\)
To find the value of c that makes the expression a perfect square, we must complete the square.
We have then:
\(x ^ 2 + 7x + (\frac{7}{2}) ^ 2
\)
Rewriting we have:
\(x ^ 2 + 7x +\frac{49}{4}\)
Therefore the value of c is given by:
\(c = \frac{49}{4}
\)
Then, the expression written as a binomial is:
\((x + \frac{7}{2}) ^ 2
\)
Answer:
the value of c that makes the expression to perfect square trinomial is:
\(c = \frac{49}{4}
\)
The expression as the square of a binomial is:
\((x + \frac{7}{2}) ^ 2\)
