+0  
 
0
118
1
avatar

Find all values of x such that  x/(x + 4) = -9/(x + 5). If you find more than one value, then list your solutions in increasing order, separated by commas.

 Dec 24, 2020
 #1
avatar+117724 
+1

x / (x +4) =  -9 /( x + 5)     cross-multiply

 

x ( x + 5)  = -9 ( x + 4)     simplify

 

x^2 + 5x   =  -9x  - 36         rearrange as

 

x^2  + 14x + 36  =  0       complete the square on x

 

x^2  + 14x   =   -36           take 1/2  of 14  =7.....square this =  49....add to both sides

 

x^2 + 14x + 49  = -36 + 49            factor the left, simplify the right

 

(x + 7)^2  =  13            take both roots

 

x+ 7  = sqrt (13)     or        x + 7   =  -sqrt (13)

 

x = sqrt (13) - 7        or       x  =  -sqrt (13)  - 7

 

 

cool cool cool

 Dec 24, 2020

9 Online Users