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Find all solutions to (x + 4)/(x + 5) = (x + 5)/(2x).

 Jul 5, 2021
 #1
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Using the quadratic equation, the answers are 1 + √26 and 1 - √26

 Jul 5, 2021
 #2
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(x +  4)  / ( x + 5)  = ( x + 5)  / (2x)      cross-multiply

 

2x ( x + 4)  =   ( x + 5) ( x + 5)

 

2x^2  + 8x  =   x^2  + 10x  + 25       rearrange  as

 

x^2 - 2x    =    25                complete  the square on x

 

x^2  - 2x   + 1   =  25 +  1

 

(x - 1)^2  =   26             take  both roots

 

x  - 1  = ±sqrt (26)

 

x =   1  ±  sqrt (26)

 

cool cool cool

 Jul 5, 2021

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