anonymous 5 years ago need help one more time on solving quadratic equation

1. anonymous

ok

2. anonymous

$y ^{2}=-24y+144$ and so far I have $-3 + or -\sqrt{57}\over -12$

3. anonymous

I'm sure it's supposed to simplify from there but not sure exactly how. Or if this will give me 2 non real answers, or 2 real ones

4. anonymous

3 and 19 make 57

5. anonymous

$-24\pm \sqrt{b ^{}}$

6. anonymous

I got 0 under radical so -24+ -0/2

7. anonymous

-12

8. anonymous

ok, so -24 + and - -12 are the non real answers?

9. anonymous

wait! I just realized I typed the wrong problem..

10. anonymous

I used +144 not -144 sorry my oversight

11. anonymous

Sorryy, can you guys wait a sec while I put the right one up here

12. anonymous

Mary, when you're solving these, be sure to get them in the form $ax^2 + bx + c = 0$ before plugging into the quadratic equation

13. anonymous

$-6^{2}+3x+2=0$

14. anonymous

So what is a, b, and c?

15. anonymous

b is 3 and c is 2

16. anonymous

I'm guessing that first term should be $$-6x^2$$

17. anonymous

so a is?

18. anonymous

oh yeah, sorry i thought you just asked about b and c

19. anonymous

a is -6

20. anonymous

Ok, now what do you get when you plug them in?

21. anonymous

the formula we have been going off of is a bit different than that. But I had gotten -3 + and - root 57 over -12

22. anonymous

$x=\frac{-3 \pm \sqrt{9-4(-6)(2)}}{2(-6)}$ $x = \frac{-3 \pm \sqrt{9+48}}{-12}$ $x = \frac{3 \pm \sqrt{57}}{12}$

23. anonymous

24. anonymous

sorry ya'll numbers all wrong I will leave

25. anonymous

don't forget -3

26. anonymous

ok so I had the right answer, except it's positive 3, not negative?

27. anonymous

are they real or non real solutions?

28. anonymous

You can simplify a bit further, but it's not gonna be a whole number or even a rational one. $x = \frac{3 \pm \sqrt{57}}{12}$ $x = \frac{3}{12} \pm \frac{\sqrt{57}}{12}$ $x = \frac{1}{4} \pm \frac{\sqrt{57}}{12}$

29. anonymous

They are real solutions. You only get non-real solutions when the thing under the square root is negative.

30. anonymous

As for the -3, if you factor a -1 from the top and bottom you can cancel to get a positive 3 on top and a 12 on bottom. So it's going to be positive. It doesn't matter much though because one of your x will be positive and one is negative.

31. anonymous

Your answer was also correct, but could be simplified a little bit.

32. anonymous

ok, thanks!

33. anonymous

because the - was common to both the numerator and denominator.