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Equations where the exponent of the first (highest degree) term is twice the exponent of the middle term are equations of "quadratic form". And they can be solved in a similar way.
It can help to use a temporary variable:
Let
Then
Substituting these into our equation we get:
It now looks like a quadratic equation. We can go ahead an solve for q. Factoring we get:
From the Zero Product Property:
2q+3 = 0 or 3q-8 = 0
2q = -3 or 3q = 8
q = -3/2 or q = 8/3
But we are not interested in a value for q. We are interested in x. So we now substitute back for x:
or
To solve for x we just cube both sides:
or
or
P.S. Once you have some practice with these quadratic form equations, you will not need a temporary variable. You will see how to factor
into
etc.
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