SOLUTION: Trying to solve: 8^x^2 = 2^x+4 (8 raised to the x power which is squared equals 2 raised to the x+4 power

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Question 210168This question is from textbook calculus with applications
: Trying to solve:

8^x^2 = 2^x+4
(8 raised to the x power which is squared equals 2 raised to the x+4 power This question is from textbook calculus with applications

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
8%5Ex%5E2+=+2%5E%28%28x%2B4%29%29 Substitute 8+=+2%5E3
%282%5E3%29%5Ex%5E2+=+2%5E%28%28x%2B4%29%29 Simplify the left side.
2%5E%283x%5E2%29+=+2%5E%28%28x%2B4%29%29 Now since the bases are equal (2) the exponents are equal,so...
3x%5E2+=+x%2B4 Subtract (x+4) from both sides.
3x%5E3-x-4+=+0 Factor this trinomial.
%283x-4%29%28x%2B1%29+=+0 Apply the zero product rule.
3x-4+=+0 or x%2B1+=+0 which means that...
3x+=+4 and highlight%28x+=+4%2F3%29 or highlight%28x+=+-1%29