## poopsiedoodle Group Title How might one go about doing this problem? Solve for x: x^2 + 24x + 90 = 0 one year ago one year ago

1. nooce Group Title

Factor first :)

2. nooce Group Title

What factors of 90, when added together, give you 24?

3. poopsiedoodle Group Title

Gimme a second.

4. nooce Group Title

5. poopsiedoodle Group Title

I don't think any do. 18 and 5 is the closest you can get to 24, which is 23.

6. nooce Group Title

Hmm, hold on a sec

7. poopsiedoodle Group Title

I will do that.

8. nooce Group Title

Well, since it isn't factorable, we have to use the quadratic formula. Have you learned it?

9. poopsiedoodle Group Title

Hardly. I've just started on it.

10. nooce Group Title

Well, this may take some explaining to do, so hold on for a bit haha.

11. nooce Group Title

x^2 + 24x + 90 = 0 Let's break down what this problem means. By plugging in a certain number(s) for x, you get zero. It's pretty much like plotting a graph of x^2 + 24x + 90 and looking for where the graph touches zero. Did I lose you yet?

12. nooce Group Title

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13. poopsiedoodle Group Title

Okay. I get it so far.

14. nooce Group Title

Alright. So since we have an equation that isn't factorable, we find the zeroes by plugging it into the quadratic formula.

15. nooce Group Title

This is the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac} }{ 2a }$ Now, a, b, and c are the numbers in your equation -- $a^2+bx+c$ In this case: $x^2 + 24x + 90$ so, a=1, b= 24, and c=90.

16. poopsiedoodle Group Title

Ok, lemme try it now.

17. nooce Group Title

Remember, the ± symbol indicates that there are two expressions! (ex. 1 ± 3 is 1 + 3 AND 1 - 3)

18. poopsiedoodle Group Title

$\Large0= \frac{ -24 \pm \sqrt{24^{2} -4(90)} }{ 2 }$

19. nooce Group Title

Good so far!

20. nooce Group Title

except, it's x =

21. poopsiedoodle Group Title

Well, since we're already using x in the original problem, how about Y?

22. nooce Group Title

But we're trying to solve for x, haha

23. poopsiedoodle Group Title

eh, whatever. By the way, I'm having a slight problem with $\sqrt{4(90)}$

24. nooce Group Title

That's just $\sqrt{4 • 90} = \sqrt{360}$

25. poopsiedoodle Group Title

Ah. $\Large x= \frac{ -24 \pm 24\sqrt{360} }{ 2 }$

26. nooce Group Title

No, remember 24^2 is under the radical (Don't take it out!) $\sqrt{24^2 - 360}$

27. poopsiedoodle Group Title

$\Large x= \frac{ -24 \pm \sqrt{ 24^{2} (-360)} }{ 2 }$*

28. poopsiedoodle Group Title

But, since √24^2 = 24, what's wrong with taking it out?

29. nooce Group Title

Because we can't have a negative number under a square root, haha

30. poopsiedoodle Group Title

Ah.

31. nooce Group Title

But anyways, after plugging all of those numbers in, what do you geT?

32. poopsiedoodle Group Title

So, $\Large x= { -12 \pm (\sqrt{ 24^{2} (-360)} /2)}$ ? I'm confused now e_o

33. nooce Group Title

Well, the /2 should be on the bottom of the whole thing, but besides that, Let's simplify the square root first. What is 24^2 - 360?

34. poopsiedoodle Group Title

216.

35. poopsiedoodle Group Title

and the root of that is 14.giganticdecimal

36. nooce Group Title

Well, let's simplify it haha sqrt of 216 can be reduced into what? (hint: 36 x 6 = 216)

37. poopsiedoodle Group Title

oh gee, this is a tought one... 2... and... erm... GIMME A MINUTE

38. poopsiedoodle Group Title

tough*

39. poopsiedoodle Group Title

OOH! I KNOW! 36 AND 6. BOOM. Don't you wish you had thought of that?

40. nooce Group Title

Hahahaha. You are correct x)

41. nooce Group Title

So... now we have $x = \frac{ -24 \pm 6\sqrt{6} }{ 2 }$ which breaks down to: $x = \frac{ -24 + 6\sqrt{6} }{ 2 }$ $x = \frac{ -24 - 6\sqrt{6} }{ 2 }$ I assume you can solve from there :)

42. poopsiedoodle Group Title

$\Huge x = { -12 - 3\sqrt{3} }$ ?

43. nooce Group Title

Annnnnnnnnd?

44. poopsiedoodle Group Title

I was wondering if I was right, which I guess I am. So, is it $$\Huge x=-12 -3?$$

45. nooce Group Title

Wait, no don't take out the radical 3 lol You need to solve for the other part: $x = \frac{ -24 + 6\sqrt{6} }{ 2 }$ Your first solution was correct, btw!

46. poopsiedoodle Group Title

Oh. x=-12 + 3√3. And now what do I do?

47. nooce Group Title

Well, those are your solutions, haha x=-12 + 3√3 and x=-12 - 3√3 Yay!

48. poopsiedoodle Group Title

:D

49. nooce Group Title

:D indeed! If you need more help, just pm me (: