Question

***WILL MEDAL***
Solve this equation by completing the square.
3x^2 - 4x = -2

Answer 1

Do you know the steps to complete the square?

Answer 2

no...

Answer 3

All right. Here you go. Divide the whole equation by whatever is multiplying the squared term. In this cae you have to divide everything by 3. By doing this, you have \(x^{2}-\frac{4}{3}x=\frac{-2}{3}\)

Answer 4

Then you take half of the "x" coefficient (\(\frac{4}{3}\)), square it and add to both sides.

Answer 5

Which means you will be adding \((\frac{2}{3})^{2}\) to both sides.

Answer 6

By doing this, you will have \(x^{2}-\frac{4}{3}x+ \frac{4}{9}=\frac{-2}{3}+\frac{4}{9}\)

Answer 7

Do you see that the left side can be rewritten as a perfect square?

Answer 8

yes

Answer 9

And that's it! Rewrite the left side, simplify the right side and you will *ALMOST* have your answer. Can you finish it?

Answer 10

i can try

Answer 11

Take your chances :3

Answer 12

Im trying to square the left side and its not working

Answer 13

Well, rewriting it as a square we have \((x-\frac{2}{3})^{2}\)

Answer 14

check?

Answer 15

4/9?

Answer 16

Reminder that \((a-b)^{2}=a^{2}-2ab+b^{2}\)
Moving on...
We have \((x-\frac{2}{3})^{2}=\frac{-2}{9}\) and \(x-\frac{2}{3}=±\sqrt{\frac{-2}{9}}\)
This problem WILL NOT have answers in the set of reals, ONLY in the set of complex numbers.

Answer 17

Oh. That makes more sense.

Answer 18

Does it ask for its roots?

Answer 19

No

Answer 20

Well, then there you have your answer. :D

Answer 21

Thank you