Sum of 2 consecutive integers is $x$ then their product will be?

Question

According to a source, the answer is $x^2-\frac{1}{4}$

Please explain

Answer 1

Let the consecutive integers be $a$,$a+1$...

Now,$a+(a+1)=x\implies a=\frac{x-1}{2}\implies (a+1)=\frac{x+1}{2}$

Hence, $a(a+1)=\frac{x-1}{2}*\frac{x+1}{2}=\frac{x^2-1}{4}$

Answer 2

Let $n$ be the first of those consecutive numbers. Then we have: $$ n + (n+1) = x $$

which implies $ n= \frac{x-1}{2}$

using that you can calculate the product of $n(n+1)$