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

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nooceBest ResponseYou've already chosen the best response.1
What factors of 90, when added together, give you 24?
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
I don't think any do. 18 and 5 is the closest you can get to 24, which is 23.
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Well, since it isn't factorable, we have to use the quadratic formula. Have you learned it?
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
Hardly. I've just started on it.
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Well, this may take some explaining to do, so hold on for a bit haha.
 one year ago

nooceBest ResponseYou've already chosen the best response.1
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?
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
Okay. I get it so far.
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Alright. So since we have an equation that isn't factorable, we find the zeroes by plugging it into the quadratic formula.
 one year ago

nooceBest ResponseYou've already chosen the best response.1
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.
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
Ok, lemme try it now.
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Remember, the ± symbol indicates that there are two expressions! (ex. 1 ± 3 is 1 + 3 AND 1  3)
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
\[\Large0= \frac{ 24 \pm \sqrt{24^{2} 4(90)} }{ 2 }\]
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
Well, since we're already using x in the original problem, how about Y?
 one year ago

nooceBest ResponseYou've already chosen the best response.1
But we're trying to solve for x, haha
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
eh, whatever. By the way, I'm having a slight problem with \[\sqrt{4(90)}\]
 one year ago

nooceBest ResponseYou've already chosen the best response.1
That's just \[\sqrt{4 • 90} = \sqrt{360}\]
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
Ah. \[\Large x= \frac{ 24 \pm 24\sqrt{360} }{ 2 }\]
 one year ago

nooceBest ResponseYou've already chosen the best response.1
No, remember 24^2 is under the radical (Don't take it out!) \[\sqrt{24^2  360}\]
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
\[\Large x= \frac{ 24 \pm \sqrt{ 24^{2} (360)} }{ 2 }\]*
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
But, since √24^2 = 24, what's wrong with taking it out?
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Because we can't have a negative number under a square root, haha
 one year ago

nooceBest ResponseYou've already chosen the best response.1
But anyways, after plugging all of those numbers in, what do you geT?
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
So, \[\Large x= { 12 \pm (\sqrt{ 24^{2} (360)} /2)}\] ? I'm confused now e_o
 one year ago

nooceBest ResponseYou've already chosen the best response.1
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?
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
and the root of that is 14.giganticdecimal
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Well, let's simplify it haha sqrt of 216 can be reduced into what? (hint: 36 x 6 = 216)
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
oh gee, this is a tought one... 2... and... erm... GIMME A MINUTE
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
OOH! I KNOW! 36 AND 6. BOOM. Don't you wish you had thought of that?
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Hahahaha. You are correct x)
 one year ago

nooceBest ResponseYou've already chosen the best response.1
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 :)
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
\[\Huge x = { 12  3\sqrt{3} }\] ?
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
I was wondering if I was right, which I guess I am. So, is it \(\Huge x=12 3?\)
 one year ago

nooceBest ResponseYou've already chosen the best response.1
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!
 one year ago

poopsiedoodleBest ResponseYou've already chosen the best response.1
Oh. x=12 + 3√3. And now what do I do?
 one year ago

nooceBest ResponseYou've already chosen the best response.1
Well, those are your solutions, haha x=12 + 3√3 and x=12  3√3 Yay!
 one year ago

nooceBest ResponseYou've already chosen the best response.1
:D indeed! If you need more help, just pm me (:
 one year ago
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