+0  
 
-3
88
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avatar+104 

Find the number that can be placed in the empty space below so that the resulting quadratic is the square of a binomial:
 

x^2 + 22x + __

 

thanks !

 Mar 20, 2020
 #1
avatar+1956 
+3

Sorry I'm not CPhill.... but I'll try my best, too!

 

We know that in order to get a square of a binomial, we have to do (b/2)^2.

 

In this case, that will get us (22/2)^2 which is 121.

 

Therefore, we need to add 121 to each side, which will eventually get us (x+11)^2.

 

Hope this helped!

 Mar 20, 2020
 #2
avatar+23566 
+2

This is 'completing the square '  exercise'

take 1/2 of the 'x' coefficient     then square it    11^2 = 121

 

x^2 + 22x + 121    =    (x+11)2

 Mar 20, 2020
 #3
avatar+104 
0

hm.. neither of those answers are right.

 Mar 20, 2020
 #4
avatar+23566 
+2

The number to place in the blank is    '  121  '  cheeky

ElectricPavlov  Mar 20, 2020
 #5
avatar+104 
0

ohh! thank you EP:))

matthewmacdell  Mar 20, 2020
 #6
avatar+1956 
+1

Yup! We're adding the 121 to each side, right?

CalTheGreat  Mar 21, 2020
 #7
avatar+109509 
+1

Attn: CalTheGreat

 

There is only one side 

 

This is NOT an equation.

 

All you are being asked is, 'what number do you need to add to   x^2 +22x    in order to make the expression a perfect square'.

 

the answer is   \((\frac{22}{2})^2 = 11^2 = 121\)

 

 

\(x^2+22x+\boxed{121} = (x+11)^2\)

Melody  Mar 21, 2020
 #8
avatar+1956 
+2

Melody, you're right! Thanks for correcting me!

CalTheGreat  Mar 21, 2020

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