poopsiedoodle
  • poopsiedoodle
How might one go about doing this problem? Solve for x: x^2 + 24x + 90 = 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Factor first :)
anonymous
  • anonymous
What factors of 90, when added together, give you 24?
poopsiedoodle
  • poopsiedoodle
Gimme a second.

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anonymous
  • anonymous
Take your time (:
poopsiedoodle
  • poopsiedoodle
I don't think any do. 18 and 5 is the closest you can get to 24, which is 23.
anonymous
  • anonymous
Hmm, hold on a sec
poopsiedoodle
  • poopsiedoodle
I will do that.
anonymous
  • anonymous
Well, since it isn't factorable, we have to use the quadratic formula. Have you learned it?
poopsiedoodle
  • poopsiedoodle
Hardly. I've just started on it.
anonymous
  • anonymous
Well, this may take some explaining to do, so hold on for a bit haha.
anonymous
  • anonymous
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?
anonymous
  • anonymous
|dw:1358120873885:dw|
poopsiedoodle
  • poopsiedoodle
Okay. I get it so far.
anonymous
  • anonymous
Alright. So since we have an equation that isn't factorable, we find the zeroes by plugging it into the quadratic formula.
anonymous
  • anonymous
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.
poopsiedoodle
  • poopsiedoodle
Ok, lemme try it now.
anonymous
  • anonymous
Remember, the ± symbol indicates that there are two expressions! (ex. 1 ± 3 is 1 + 3 AND 1 - 3)
poopsiedoodle
  • poopsiedoodle
\[\Large0= \frac{ -24 \pm \sqrt{24^{2} -4(90)} }{ 2 }\]
anonymous
  • anonymous
Good so far!
anonymous
  • anonymous
except, it's x =
poopsiedoodle
  • poopsiedoodle
Well, since we're already using x in the original problem, how about Y?
anonymous
  • anonymous
But we're trying to solve for x, haha
poopsiedoodle
  • poopsiedoodle
eh, whatever. By the way, I'm having a slight problem with \[\sqrt{4(90)}\]
anonymous
  • anonymous
That's just \[\sqrt{4 • 90} = \sqrt{360}\]
poopsiedoodle
  • poopsiedoodle
Ah. \[\Large x= \frac{ -24 \pm 24\sqrt{360} }{ 2 }\]
anonymous
  • anonymous
No, remember 24^2 is under the radical (Don't take it out!) \[\sqrt{24^2 - 360}\]
poopsiedoodle
  • poopsiedoodle
\[\Large x= \frac{ -24 \pm \sqrt{ 24^{2} (-360)} }{ 2 }\]*
poopsiedoodle
  • poopsiedoodle
But, since √24^2 = 24, what's wrong with taking it out?
anonymous
  • anonymous
Because we can't have a negative number under a square root, haha
poopsiedoodle
  • poopsiedoodle
Ah.
anonymous
  • anonymous
But anyways, after plugging all of those numbers in, what do you geT?
poopsiedoodle
  • poopsiedoodle
So, \[\Large x= { -12 \pm (\sqrt{ 24^{2} (-360)} /2)}\] ? I'm confused now e_o
anonymous
  • anonymous
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?
poopsiedoodle
  • poopsiedoodle
216.
poopsiedoodle
  • poopsiedoodle
and the root of that is 14.giganticdecimal
anonymous
  • anonymous
Well, let's simplify it haha sqrt of 216 can be reduced into what? (hint: 36 x 6 = 216)
poopsiedoodle
  • poopsiedoodle
oh gee, this is a tought one... 2... and... erm... GIMME A MINUTE
poopsiedoodle
  • poopsiedoodle
tough*
poopsiedoodle
  • poopsiedoodle
OOH! I KNOW! 36 AND 6. BOOM. Don't you wish you had thought of that?
anonymous
  • anonymous
Hahahaha. You are correct x)
anonymous
  • anonymous
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 :)
poopsiedoodle
  • poopsiedoodle
\[\Huge x = { -12 - 3\sqrt{3} }\] ?
anonymous
  • anonymous
Annnnnnnnnd?
poopsiedoodle
  • poopsiedoodle
I was wondering if I was right, which I guess I am. So, is it \(\Huge x=-12 -3?\)
anonymous
  • anonymous
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!
poopsiedoodle
  • poopsiedoodle
Oh. x=-12 + 3√3. And now what do I do?
anonymous
  • anonymous
Well, those are your solutions, haha x=-12 + 3√3 and x=-12 - 3√3 Yay!
poopsiedoodle
  • poopsiedoodle
:D
anonymous
  • anonymous
:D indeed! If you need more help, just pm me (:

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