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What is the sum of all possible values of $x$ such that $2x(x-10)=-50$?

 Oct 7, 2022
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What is the sum of all possible values of $x$ such that $2x(x-10)=-50$?  

 

First, multiply it out.                2x2 – 20x  =  –50  

 

Add 50 to both sides              2x2 – 20x + 50  =  0  

 

We don't have to, but let's 

divide both sides by 2               x2 – 10x + 25  =  0   

 

Factor the quadratic                 (x – 5)(x – 5)  =  0  

 

The only value is                        x  =  5  

 

Or if your class counts both roots, even though they're the same, then it's 10.  

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 Oct 7, 2022

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