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Find $a$ such that $ax^2+12x+9$ is the square of a binomial.

Lightning  Jun 5, 2018
 #1
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I've seen these questions before. If these are homework problems, this is not a homework site!

smileysmiley

tertre  Jun 5, 2018
 #2
avatar+793 
+1

Hey Lightning, \(a=4\)

 

\(4x^2+12x+9\\ =(2x+3)^2\)

 

I used: \((x+y)^2=x^2+2xy+y^2\)

 

I saw the nine, so I know \(y=3\)

 

\(2xy=12\), and \(y=3\), so \(x=2\)

 

\(2^2=4, a=4\)

 

I hope this helped,

 

Gavin

GYanggg  Jun 5, 2018

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