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

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

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

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

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

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

nooce
 one year ago
Best ResponseYou've already chosen the best response.1x^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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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