if 3x^2 – 2x 7 = 0, then ( x – 1/3 ) ^2 = ?

Question

Given the equation (3x^2 - 2x - 7 = 0), how can I determine the value of ((x - \frac{1}{3})^2)?

Anonymous · Accepted Answer

3x&sup2; &ndash; 2x + 7 = 03x&sup2; &ndash; 2x = &ndash; 7x&sup2; &ndash; 2/3x = &ndash; 7/3x&sup2; &ndash; 1/3x = &ndash; 7/3 + (1/3)&sup2;x&sup2; &ndash; 1/3x = &ndash; 21/9 + 1/9(x &ndash; 1/3)&sup2; = &ndash; 20/9Answer: (x &ndash; 1/3)&sup2; = &ndash; 20/9

Fern Kirlin · Answer

I agree with Como.
You should separate it into 3 times (x^2 – (2/3)x + (7/3) = 0
Because it can be done using the quadratic formula now that it is separated into x square x and a number, which are respectively a, b, and c. And then after the quadratic formula, you can multiply the answers you get by 3.

Anonymous · Answer

3x 2 2x 7

Anonymous · Answer

3x 2-2x 7 0

Anonymous · Answer

3x² – 2x + 7 = 0
3(x² – (2/3)x + 7/3) = 0
x² – (2/3)x + 7/3 = 0
x² – (2/3)x + 1/9 = 1/9 – 7/3
(x – 1/3)² = – 20/9

Anonymous · Answer

https://shorturl.im/RDqKI
x = (2 +/- i*sqrt80)/6. x = (1 +/- i*sqrt20)/3. (x – (1/3))^2 = (1/3 + i*sqrt(20)/3 – 1/3)^2 = -20/9. (x – (1/3))^2 = (1/3 – i*sqrt(20)/3 – 1/3)^2 = -20/9. Answer: -20/9 or -2 2/9. -John

Anonymous · Answer

first, find x.  Quadratic formula would probably be easiest.
(2 + / – sqrt (4 – 84)) / 6
(2 + / – sqrt (-80)) / 6
(2 + / – 4i(sqrt5) / 6
x=(1 + 2i(sqrt5)) / 3 OR (1 – 2i(sqrt5)) / 3
((1 + 2i(sqrt5)) / 3 – 1/3)^2 = (((2i(sqrt5))/3)^2) = -20/9
((1 – 2i(sqrt5))/3 – 1/3)^2 = (((-2i(sqrt5))/3)^2) = -20/9
-20/9.  Man, that was a workout!
BTW Jon Agruda got the right answer . . . but I question his methods a little bit, looks like he randomly put a (1/3)^2 in there about the fourth line.  also, last step, he says that x^2 – (1/3)x = (x-1/3)^2, that is not true.  But then again, he is a top contributor so I’m not sure, but I know my methodology is right.

Anonymous · Answer

What is 2x 7, did you miss a sign?

Anonymous

if 3x^2 – 2x 7 = 0, then ( x – 1/3 ) ^2 = ?

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