Find all real values of $s$ such that $x^2 + sx + 144 - 44$ is the square of a binomial.

learnmgcat May 27, 2024

#1**+1 **

First off, let's combine like terms to get \(x^2 + sx + 100\).

For this to be a square of a binomial, we must recognize that s is equal to double the square root of 100.

Solving this we get s=20.

Indeed, \(x^2+20x+100 = (x+10)^2\).

However, we also get s=-20.

We have \(x^2-20x+100 = (x-10)^2\).

This means s=-20, 20

Thanks! :)

(Haha, this is the post that got me to 200 points!)

NotThatSmart May 27, 2024