### Instruction: If $c$ is a constant such that $x^2+100x+c$ is equal to the square of a binomial, then what is $c$?### Response: 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 $c=50^2=2500$.