## Falling_In_Katt one year ago ***WILL MEDAL*** Solve this equation by completing the square. 3x^2 - 4x = -2

1. ChillOut

Do you know the steps to complete the square?

2. Falling_In_Katt

no...

3. ChillOut

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 $$x^{2}-\frac{4}{3}x=\frac{-2}{3}$$

4. ChillOut

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

5. ChillOut

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

6. ChillOut

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

7. ChillOut

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

8. Falling_In_Katt

yes

9. ChillOut

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

10. Falling_In_Katt

i can try

11. ChillOut

12. Falling_In_Katt

Im trying to square the left side and its not working

13. ChillOut

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

14. ChillOut

check?

15. Falling_In_Katt

4/9?

16. ChillOut

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.

17. Falling_In_Katt

Oh. That makes more sense.

18. ChillOut

Does it ask for its roots?

19. Falling_In_Katt

No

20. ChillOut