If $c$ is a constant such that $x^2+100x+c$ is equal to the square of a binomial, then what is $c$?
I know that the square of a binomial has the form $(x+a)^2=x^2+2ax+a^2$, where $a$ is some constant. So I want to find a value of $c$ that makes $x^2+100x+c$ match this form. That means I need to have $100x=2ax$, so $a=50$. Then I also need to have $c=a^2$, so $c=50^2=2500$. 