Answer :
Answer: [tex]c=\frac{49}{4}[/tex]
Step-by-step explanation:
You can find the value of "c" that will make it a perfect square trinomial by Completing the square.
Given the following expression provided in the exercise:
[tex]x^2 - 7x + c[/tex]
You can notice that it is written in this form:
[tex]ax^2-bx+c[/tex]
Then, you can identify that the coefficient "b" is:
[tex]b=-7[/tex]
Since to complete the square you must add and subtract the half of square of coefficient "b", you can conclude that:
[tex]c=(\frac{b}{2})^2[/tex]
Therefore, substituting "b" into [tex]c=(\frac{b}{2})^2[/tex], you get:
[tex]c=(\frac{-7}{2})^2\\\\c=\frac{49}{4}[/tex]