If 3x^2-2x+7=03x2−2x+7=0, what is (x-1/3)^2(x−13)2?

2 Answers
Robert C.
Jul 30, 2016

not sure what you're needing here

Explanation:

is this a substitution question?

George C.
Jul 30, 2016

(x-1/3)^2 = -20/9(x−13)2=−209

Explanation:

0 = 3x^2-2x+70=3x2−2x+7

= 3(x^2-2/3+7/3)=3(x2−23+73)

= 3((x-1/3)^2-1/9+7/3)=3((x−13)2−19+73)

= 3((x-1/3)^2+20/9)=3((x−13)2+209)

Hence (x-1/3)^2 = -20/9(x−13)2=−209

So x-1/3 = +-sqrt(-20/9) = +-(2sqrt(5))/3ix−13=±√−209=±2√53i

So x=1/3+-(2sqrt(5))/3ix=13±2√53i

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