SOLUTION: Solve for x: 2(8)^(4x)-33(8)^(2x)+16=0

Question 135305: Solve for x: 2(8)^(4x)-33(8)^(2x)+16=0
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Solve for x:

Let's temporarily substitute and
This can be solved for z by factoring.
and...
and , so we have...
so that:
and

Now we replace the z with , so...
but and , so, making these substitutions, we get:
Simplify the left side.
Applying the rule: If then , so...
Divide both sides by 6.
This is one of the roots.
Substitute
Substitute: and
Simplify the left side.
or...
Divide both sides by 6.
Simplify.
This is the second root.
Solution is:

I'll leave the check for you to do. It's not difficult and I've done it myself and the two solutions for x are indeed valid!
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