Why make stupid calcul when

thinking a little more, you would get simple and pretty solution?!

Just have a look on your ugly equation

-b/9(-b/9(x-5)^2+b-5)^2+b=0, when you put x=5, you get

-b/9(b-5)^2+b=0, (and replace b by x, you will get EXACTLY f(x)=0)

then find b=2, while we knew already f(2)=0, a little stupid, right?

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if you know thinking math and use your brain and knowledge intelligently,

5 is unique root of ff(x) ==>if f(b)=f(5), b=5, you can get directly the other root of f(x), without knowing the expression of f(x)