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What number goes in the box so that 

\[x^2 + \boxed{\phantom{00}}x + 4\]

is the square of a binomial? If you find more than one, give your answer as a list.

 Jun 13, 2021
 #1
avatar+2205 
+1

Try expanding (x+2)^2 and (x-2)^2 and see what you get. :))

 

=^._.^=

 Jun 13, 2021
 #2
avatar+121056 
+2

Let   the   middle  term  =  bx

 

Completing the  square  on this term  would  give us

 

(b  / 2)^2    = 4

 

b^2  / 4   =  4

 

b^2   =   16       take both roots

 

b = 4      or     b  =   -4

 

 

cool cool cool

 Jun 13, 2021

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