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Portia solved the quadratic equation $x^2+(2\sqrt3)x+1=0$ by completing the square. In the process, she came up with the equivalent equation $$(x+r)^2 = s,$$where $r$ and $s$ are constants. What is $s$?

Lightning  Jun 3, 2018
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Portia solved the quadratic equation \(x^2+(2\sqrt3)x+1=0\) by completing the square. In the process, she came up with the equivalent equation \((x+r)^2 = s\),where r and s are constants. What is s?

 

If you don't know how to complete a square, check out this website: https://www.mathsisfun.com/algebra/completing-square.html

 

However, if you're just stuck on this question, you can view my solution here:

 

We can complete the square by adding 2 to both sides. 

 

\(x^2+(2\sqrt3)x+3=2\\ (x+\sqrt3)^2=2\\ \)

From this, we can tell:

 

\(r=\sqrt3\\ s=2\)

 

The answer you seek is 2, 

 

I hope this helped,

 

Gavin

GYanggg  Jun 3, 2018

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