## anonymous 5 years ago Use quadratic formula to solve for y 3x^2- 2(sqrt3)xy +y^2 +6(sqrt3)x -2y -40=0

1. myininaya

so we can put y in terms of x?

2. myininaya

$(1)y^2+(-2 \sqrt{3}x-2)y+(3x^2+6 \sqrt{3}x-40)=0$

3. myininaya

$\text{ where }a=1, b=-2 \sqrt{3}-2 , c=3x^2+6 \sqrt{3} x-40$

4. myininaya

$y=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

5. anonymous

well the option that is closest to what i get when i plug those in is y=1+sqrt3(x) +/- sqrt(-4sqrt3(x) =41)

6. myininaya

$y=\frac{-(-2 \sqrt{3}-2) \pm \sqrt{(-2 \sqrt{3}-2)^2-4(1)(3x^2+6 \sqrt{3}x-40)}}{2(1)}$

7. myininaya

this is crazy lookin' lol

8. myininaya

$y=\frac{2 \sqrt{3} +2 \pm \sqrt{4(3)-2(-2 \sqrt{3} (2))+2^2-12x^2-24 \sqrt{3} x+160}}{2}$

9. anonymous

haha yes i know! that is what i got when i plugged them in. However, i have multiple choice, and t hat is not an option. $y= 1+ \sqrt{3}x \pm \sqrt{-4\sqrt{3}x +41}$

10. anonymous

this is the only similar option

11. myininaya

$y=\frac{2 \sqrt{3} +2 \pm \sqrt{12+8 \sqrt{3}+4-12x^2-24 \sqrt{3} x+160}}{2}$

12. anonymous

idk its not one of my options :(

13. myininaya

$y=\frac{2 \sqrt{3}+2 \pm \sqrt{-12x^2-24 \sqrt{3}x+176+8 \sqrt{3}}}{2}$ i'm still simplying i'm just showing my steps

14. myininaya

simplifying*

15. anonymous

oh okay! sorry!

16. myininaya

$y=\frac{2 \sqrt{3}+2 \pm \sqrt{4} \sqrt{-3x^2-6 \sqrt{x} +44+2 \sqrt{3}}}{2}$

17. myininaya

$y=\frac{2 \sqrt{3} +2 \pm 2 \sqrt{-3x^2-6 \sqrt{x}+44+2 \sqrt{3}}}{2}$

18. myininaya

notice each term has the common factor 2

19. myininaya

$y=\frac{ \sqrt{3}+1 \pm 1 \sqrt{-3x^2-6 \sqrt{x}+44+2 \sqrt{3}}}{1}$ $y= \sqrt{3}+1 \pm \sqrt{-3x^2-6 \sqrt{x}+44+2 \sqrt{3}}$

20. myininaya

oops i'm missing x in my b term

21. myininaya

:(

22. myininaya

i have to do this on paper lol

23. myininaya

can you give me a sec?

24. anonymous

its alright! of course i can! do you think when you are done you could help me with another similar problem?

25. myininaya

ok i got it

26. myininaya

i'm gonna scan it

27. anonymous

ok:)

28. myininaya

29. myininaya

which is what you thought gj

30. anonymous

yes! thank you so much

31. myininaya

that is weird the file posted twice

32. myininaya

how many times do you see the file?

33. myininaya

it keeps posting :(

34. anonymous

like 5 at least haha

35. myininaya

ok i have to do something post your new question on the left ok and if i get back i will look at it

36. anonymous

okay! i will.

37. myininaya

:) fun problem by the way

38. anonymous

haha yes it was! thanks for your help!