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Krzysztof solved the quadratic equation \( 11x^2-44x-99=0\) by completing the square. In the process, he came up with the equivalent equation \((x+r)^2 = s\) where r and s are constants.

What is r+s?

 

Found the root: \(x = 3 ± i √ 57\) . Don't understand how to move on with this.

 Oct 14, 2019
edited by AoPS.Morrisville  Oct 14, 2019
 #1
avatar+109202 
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11x^2 -44x  - 99 = 0       divide through by 11

 

x^2 - 4x - 9  = 0      add 9 to both sides

 

x^2 - 4x  =  9       take 1/2 of 4 = 2....square it = 4....add to both sides

 

x^2 - 4x + 4  =   9 + 4          factor the left.....simplify the right

 

(x - 2)^2  =  13

 

( x +  -2)^2  = 13

 

r =  -2        s  = 13

 

So... r + s  =   11

 

 

cool cool cool

 Oct 14, 2019
 #2
avatar+148 
-1

Thank You so much for explaining how to work through.

 Oct 14, 2019
 #3
avatar+109202 
0

OK, man....no prob   !!!

 

 

cool cool cool

CPhill  Oct 14, 2019

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