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The key to solving this is to notice that the exponent of 2 in the first term is twice the exponent of the exponent of 2 in the middle term. That makes this equation a quadratic equation in . If you have trouble seeing this, let's use a temporary variable. Let , then Substituting into the original equation we get:
The quadratic nature of the equation should now be clear. We can solve for q by factoring (or using the Quadratic Formula):
Using the Zero Product Property: or
Solving we get: or
Now we can substitute back for the temporary variable: or
From the first equation we can see that x must be 3. And since 2 to any power can never be negative, there is no solution for .
So the only solution to
is
x = 3
With some practice you will no longer need a temporary variable. You will be able to go straight from
to
(