SOLUTION: what is x? 3^(2x+1)+(28*3^(x))+9=0

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Question 163907: what is x? 3^(2x+1)+(28*3^(x))+9=0
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%282x%2B1%29%2B%2828%2A3%5E%28x%29%29%2B9=0
<=> 3%5E%282x%29%2A3%5E%281%29+%2B+28%2A3%5Ex+%2B+9+=+0
<=> 3%2A3%5E%282x%29+%2B+28%2A3%5Ex+%2B+9+=+0
let 3%5Ex+=+a, then
3%2Aa%5E2+%2B+28%2Aa+%2B+9+=+0
factorize this problem into this:
%283a+%2B+1%29%2A%28a+%2B+9%29+=+0
then we get:
3a + 1 = 0
<=> 3a = -1
<=> a = -1/3
change the variable a back to 3%5Ex
<=> 3%5Ex+=+-1%2F3
-> there is no answer for this equation
and try the other one:
a + 9 = 0
<=>a = -9
change the variable a back to 3%5Ex
<=> 3%5Ex = -9
-> there is no answer for this equation too
so this equation problem has no solution