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

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

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

nooce
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1Okay. I get it so far.

nooce
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1Ok, lemme try it now.

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

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

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

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

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

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

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

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

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

poopsiedoodle
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1and the root of that is 14.giganticdecimal

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

poopsiedoodle
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1Hahahaha. You are correct x)

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

poopsiedoodle
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1Oh. x=12 + 3√3. And now what do I do?

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