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What number must be placed in the box below so that the resulting quadratic is the square of a binomial \(x^2 - 36x + \boxed{\phantom{000}}\)

 Sep 20, 2017
 #1
avatar+98005 
+1

 

x^2  - 36x +   ???

 

Take  (1/2)  of 36  = 18  ....square it.....=  324   and this is the number...

 

Proof.....the binomial is  ( x - 18)  ...so.....

 

(x - 18)^2  =  (x - 18) (x - 18)  =  x^2   - 18x - 18x + 324   =  x^2  - 36x + 324

 

 

 

cool cool cool

 Sep 20, 2017

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