How do you solve #\frac { 2} { ( 3k - 10) ^ { 2} } + \frac { 5} { 3k - 10} + 2= 0#?

1 Answer
Matthew T.
Nov 6, 2016

#k=\frac{8}{3}or\frac{19}{6}#

Explanation:

multiply both sides by #(3k-10)^2#
#2+5(3k-10)+2(3k-10)^2=0#
expand
#2+15k-50+2(9k^2-60k+100)=0#
#15k-48+18k^2-120k+200=0#
#18k^2-105k+152=0#
qudratic formula
#k=\frac{105\pm\sqrt{(-105)^2-4(18)(152)}}{2(18)}#
#k=\frac{105\pm\sqrt{11025-10944}}{36}#
#k=\frac{105\pm\sqrt{81}}{36}#
#k=\frac{105\pm9}{36}#
#k=\frac{35\pm3}{12}#
#k=\frac{32}{12}or\frac{38}{12}#
#k=\frac{8}{3}or\frac{19}{6}#

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