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

 Dec 29, 2017
 #1
avatar+7352 
+2

2x(x - 10)   =   -50

                                             Distribute  2x  to both terms in parenthesees.

(2x)(x) + (2x)(-10)   =   -50

 

2x2 - 20x   =   -50

                                             Add  50  to both sides.

2x2 - 20x + 50   =   0

                                             Divide through by  2 .

x2 - 10x + 25   =   0

                                             Factor the left side of the equation.

(x - 5)(x - 5)  =  0

 

(x - 5)2  =  0

                                             Take the square root of both sides.

x - 5  =  0

 

x  =  5

 

The only possible value of  x  is  5 , so the sum of all the possible values is  5  .

 Dec 29, 2017
 #2
avatar+175 
+3

First we divide both sides by 2 to get \(x(x-10)=-25\). Expanding the left side and bringing the constant over, we get \(x^2-10x+25=0\) . We can factor this into \((x-5)(x-5)\), so the only possible value for \(x\)  is \(\boxed{5}\) , which is also our answer.

 Dec 29, 2017

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