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Given that $x = \frac{5}{7}$ is a solution to the equation $56 x^2 + 27 = 89x - 8,$ what is the other value of $x$ that will solve the equation? Express your answer as a common fraction.

 Dec 30, 2017
 #1
avatar+17774 
+2

56x2 + 27  =  89x - 8

56x2 - 89x + 35  =  0

Since  x = 5/7  is a solution; one factor will be  7x - 5: the other factor will be  8x - 7:

(7x - 5)(8x - 7)  =  0

Either 7x - 5  =  0     or     8x - 7  =  0

                7x  =  5                   8x  =  7

                  x  =  5/7                  x  =  7/8

 Dec 30, 2017
 #2
avatar+101234 
+2

Thanks, geno....here's one more approach

 

56x^2  +  27  =  89x  - 8   rearrange as

 

56x^2  -  89x  +  35  = 0

 

The sum of the solutions  =  89/56

 

So  letting r be the other solution, this means that

 

5/7  +  r   =  89/56

 

r  =  89/56  -  5/7

 

r  =  89/56  -  40/56

 

r  =  49 / 56   =   7 / 8  

 

 

cool cool cool

 Dec 30, 2017
edited by CPhill  Dec 30, 2017

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