# How do you find the value of c that makes x^2-19x+c into a perfect square?

$c = - {\left(\frac{19}{2}\right)}^{2}$
You square half of the 'b' term. This is because if you take the general binomial ${\left(a + b\right)}^{2}$ and expand it you get ${a}^{2} + 2 a b + {b}^{2}$. In your quadratic, we can view 'x' as the 'a' and -19 as '2a'. Thus, if -19 = 2b we divide by 2 to give us $b = - \frac{19}{2}$ and finally, we square it to give us the b squared.