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I think I complete the square but idk Rewrite the expression $4s^2 + 28s + 45$ in the form $(cs + p)^2 + q$. What is $q$?

AnonymousConfusedGuy  Oct 20, 2017
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3+0 Answers

 #1
avatar+78755 
+2

4s^2 + 28s + 45    factor out  the 4

 

4 [ s^2  + 7s  +  45/4]

 

Take (1/2) of 7  = 7/2......square this = 49/4  ....add it and subtract it

 

4 [ s^2 + 7s + 49/4 + 45/4 - 49/4 ] 

 

Factor the first three terms and simplify

 

4 [  ( s + 7/2)^2  - 1 ]

 

4(s + 7/2)^2  - 4

 

So q =  -4

 

 

cool cool cool

CPhill  Oct 20, 2017
 #2
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0

CPhill: Aren't you actually dividing by 4 in the first step and it should disappear altogether in the 2nd step (outside the bracket)?

Guest Oct 20, 2017
 #3
avatar+78755 
0

 

This would be true if we were setting the equation to 0  and solving

 

But we aren't solving anything here......we are just completing the square

 

 

cool cool cool

CPhill  Oct 20, 2017

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