x^2 - x + c

what value of c would make the equation a perfect square

To find that you have to complete the square. The formula for that is \((\frac{b}{2})^2\).

In this equation b is -1.

\((-\frac{1}{2})^2=\frac{1}{4}\)

So it would be \(x^2-x+\frac{1}{4}\).