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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