SOLUTION: Solve 2^2x+2 - 33(2^x) + 8 = 0.

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Question 1186321: Solve 2^2x+2 - 33(2^x) + 8 = 0.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


2%5E%282x%2B2%29+-+33%282%5Ex%29+%2B+8+=+0

Note the powers of 2 in the equation are 2x+2 and x. When you need to solve an equation like this, you need to get the equation in the form of a quadratic by making the larger exponent twice the smaller.

In this example, the smaller exponent is x, so you want to rewrite the equation with the larger exponent being 2x. That is easy to do:

2%5E%282x%2B2%29=%282%5E%282x%29%29%282%5E2%29=4%282%5E%282x%29%29

So rewrite the equation as

4%282%5E%282x%29%29+-+33%282%5Ex%29+%2B+8+=+0

Then factor this as a quadratic with 2%5Ex as the variable:

%284%282%5Ex%29-1%29%282%5Ex-8%29=0
4%282%5Ex-1%29=0 OR 2%5Ex-8=0

(1) 4%282%5Ex-1%29=0
4%282%5Ex%29=1
2%5Ex=1%2F4+=+1%2F2%5E2+=+2%5E%28-2%29
x+=+-2

(2) 2%5Ex-8=0
2%5Ex=8=2%5E3
x=3

ANSWERS: x=-2 or x=3

CHECK:
(1) x=-2:

(2) x=3: 2%5E%282x%2B2%29-33%282%5Ex%29%2B8=2%5E8-33%288%29%2B8=256-264%2B8=0