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The easiest solution for this equation is found by noticing that the exponent of is twice as large as the exponent of . This makes this equation in quadratic form for . So we can solve this as a quadratic equation.
To make this a little clearer, I am going to employ a temporary variable. Let . This makes and substituting these into the equation we get:
This is obviously a quadratic equation. We can solve this using factoring (or the Quadratic Formula). This factors pretty easily:
or
By the Zero Product Property we know that this (or any) product can be zero only if one of its factors is zero. Since we only have one distinct factor:
q - 2 = 0
or
q = 2
This is a solution for our temporary variable, q. To find the solution for t we can replace q with :
Raise each side to the 4th power gives:
t = 16
We can check our answer by substituting 16 for t in the original equation:
4 - 8 + 4 = 0
0 = 0 Check!
Note: After you have done a few problems like this, you will not need to use a temporary variable. You will see how to go directly from:
to
to
to
to
t = 16
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