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

 May 27, 2024
 #1
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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!)

 May 27, 2024
edited by NotThatSmart  May 27, 2024

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