The first was a typo in the post, that was not reflected in my actual calculations: It should say a^2  ab  b^2 = 0. The same typo did not show up in the x equation.
The second came from replacing every instance of a with x*b (and leaving the instances of b alone), and then factoring out all of the b^2 pieces.
And the third was the Quadratic Formula. There are actually two solutions, but the other solution corresponded to calling a the smaller number and b the larger number, which is really no different.
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