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Find all values of $x$ such that \[9 + \frac{27}{x} + \frac{8}{x^2} = 0.\]If you find more than one value, then list your solutions, separated by commas.

 Apr 17, 2020
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\( 9 + \frac{27}{x} + \frac{8}{x^2} = 0\)

answer: -1/3, -8/3

Multiply both sides by x^2

and you will get \(9 x ^2 + 27 x + 8 = 0\)

which is equal to (3x+1)(3x+8)=0

 

set 3x+1 = 0 and solve for x.

you will get -1/3

set 3x+8=0 and solve for x

you will get -8/3

 Apr 17, 2020

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