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We will use factoring to solve this. But with only two terms, it is pointless (if it is possible at all) to use factoring by grouping to solve this equation.
First get one side to be zero (by subtracting the from each side):
And then we factor. First, as always, is to factor out the greatest common factor (GCF) if it is not a 1. The GCF here is :
Now we try to factor the factor. Among the factoring patterns you learn is the pattern for difference of cubes: . This pattern may be used here since is an obvious cube and 27 is . Using an "x" for the "a" and a "3" for the "b", then pattern tells us how will factor:
which simplifies to:
With the factoring complete we can now solve. From the Zero Product Property: or or
The first two equations are simple to solve. (We should get x = 0 and x = 3.) For the third equation we must use the quadratic formula:
which simplifies as follows:
With the negative number in the square root we will get only complex number solutions from this equation. If we are not interested in complex number solutions (or if you don't even know about complex numbers) then we stop here and just use the solutions we found from the other two factors: 0 and 3. If we do want complex solutions then we continue:
which is short for: or
In standard a + bi form this would be: or
This makes the solutions, including these complex number solutions:
x = 0 or x = 3 or or
(