A quadratic's general form is:
[tex]ax^2+bx+c[/tex]
Our trinomial given is:
[tex]x^2-x+c[/tex]
From matching it with the general form, we can say that:
[tex]\begin{gathered} a=1 \\ b=-1 \end{gathered}[/tex]
For this to be a perfect square trinomial, c will take the value:
[tex]c=(\frac{b}{2})^2^{}[/tex]
We know b = -1, thus c will be:
[tex]\begin{gathered} c=(\frac{b}{2})^2 \\ c=(-\frac{1}{2})^2 \\ c=\frac{1}{4} \end{gathered}[/tex]
Thus, the value of c that will make this a perfect square trinomial:
[tex]c=\frac{1}{4}[/tex]
