SOLUTION: Solve algebraically for x: 27^(2x+1) = 94x I was told you can complete this problem by either using factoring or completing the square? But to complete the square doesn't the equa

Algebra ->  Exponents -> SOLUTION: Solve algebraically for x: 27^(2x+1) = 94x I was told you can complete this problem by either using factoring or completing the square? But to complete the square doesn't the equa      Log On


   

Question 253896: Solve algebraically for x: 27^(2x+1) = 94x
I was told you can complete this problem by either using factoring or completing the square? But to complete the square doesn't the equation need to equal ZERO? Or can you set the problem to equal ZERO? Thank you for your wonderful help.
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Unfortunately, you can't solve 27%5E%282x%2B1%29+=+94x exactly since the variable is both in the exponent and outside the exponent. So you'll have to find the approximate solution.


If on the other hand the problem is 27%5E%282x%2B1%29+=+9%5E%284x%29, then...


27%5E%282x%2B1%29+=+9%5E%284x%29 Start with the given equation.


%283%5E3%29%5E%282x%2B1%29+=+%283%5E2%29%5E%284x%29 Rewrite 27 as 3%5E3 and 9 as 3%5E2


3%5E%283%282x%2B1%29%29+=+3%5E%282%284x%29%29 Multiply the exponents.


3%5E%283%282x%2B1%29%29+=+3%5E%288x%29 Multiply


3%282x%2B1%29=8x Since the bases are equal, this means that the exponents are equal.


6x%2B3=8x Distribute.


6x=8x-3 Subtract 3 from both sides.


6x-8x=-3 Subtract 8x from both sides.


-2x=-3 Combine like terms on the left side.


x=%28-3%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=3%2F2 Reduce.


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Answer:

So the solution is x=3%2F2

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
27^(2x+1) = 94x
Are you sure you copied this right? This will involve logarithms not factoring nor completing the square.
To answer your question about equaling zero.
No it does NOT have to equal 0.
when you complete the square you just add the amount to both sides.
With any luck the amount not in the square will be a square too.