Question

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

Answer 1

`c=-(19/2)^2`

Explanation:

You square half of the 'b' term. This is because if you take the general binomial `(a+b)^2` and expand it you get `a^2+2ab+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=-19/2` and finally, we square it to give us the b squared.