+0  
 
0
89
1
avatar

Given , compute the sum of all the possible values of $\frac{14x+22}{x+2}=-3x+1$ Express your answer as a fraction.

 Apr 25, 2021
 #1
avatar+544 
0

\(\frac{14x + 22}{x + 2} = -3x + 1\)

 

\(14x + 22 = (-3x + 1)(x + 2)\)

\(14x + 22 = -3x^2 -6x + x + 2\)

\(3x^2 + 6x + 14x - x + 22 - 2 = 0\)

\(3x^2 + 19x + 20 = 0\)

 

\(x = {-(19) \pm \sqrt{(19)^2-4(3)(20)} \over 2(3)}\)

\(x = {-19 \pm \sqrt{361-240} \over 6}\)

\(x = {-19 \pm \sqrt{121} \over 6}\)

\(x = {-19 \pm 11 \over 6}\)

 

\(x = -5\)

\(x = -\frac{4}{3}\)

 

\(-5 + -\frac{4}{3} = \frac{-15 - 4}{3} = -\frac{19}{3}\)

.
 Apr 25, 2021

11 Online Users

avatar