To determine the value of \( c \) that will make the expression \( x^2 - 7x + c \) a perfect square trinomial, we can use the formula for a perfect square trinomial:
\[ (x - \frac{b}{2})^2 = x^2 - bx + \left(\frac{b}{2}\right)^2 \]
For the expression \( x^2 - 7x + c \), we know \( b = -7 \).
First, we calculate \( \frac{b}{2} \):
\[ \frac{-7}{2} = -\frac{7}{2} \]
Next, we square this value:
\[ \left(-\frac{7}{2}\right)^2 = \frac{49}{4} \]
So, to make the expression \( x^2 - 7x + c \) a perfect square trinomial, the value of \( c \) must be:
\[ c = \frac{49}{4} \]
Thus, the value of \( c \) that makes the expression a perfect square trinomial is:
\[ \frac{49}{4} \]