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

Mathematics
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Factor first :)
What factors of 90, when added together, give you 24?
Gimme a second.

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Other answers:

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

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