Question

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

Answer 1

Factor first :)

Answer 2

What factors of 90, when added together, give you 24?

Answer 3

Gimme a second.

Answer 4

Take your time (:

Answer 5

I don't think any do. 18 and 5 is the closest you can get to 24, which is 23.

Answer 6

Hmm, hold on a sec

Answer 7

I will do that.

Answer 8

Well, since it isn't factorable, we have to use the quadratic formula.

Have you learned it?

Answer 9

Hardly. I've just started on it.

Answer 10

Well, this may take some explaining to do, so hold on for a bit haha.

Answer 11

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?

Answer 12

Okay. I get it so far.

Answer 13

Alright. So since we have an equation that isn't factorable, we find the zeroes by plugging it into the quadratic formula.

Answer 14

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.

Answer 15

Ok, lemme try it now.

Answer 16

Remember, the ± symbol indicates that there are two expressions!
(ex. 1 ± 3 is 1 + 3 AND 1 - 3)

Answer 17

\[\Large0= \frac{ -24 \pm \sqrt{24^{2} -4(90)} }{ 2 }\]

Answer 18

Good so far!

Answer 19

except, it's x =

Answer 20

Well, since we're already using x in the original problem, how about Y?

Answer 21

But we're trying to solve for x, haha

Answer 22

eh, whatever. By the way, I'm having a slight problem with \[\sqrt{4(90)}\]

Answer 23

That's just
\[\sqrt{4 • 90} = \sqrt{360}\]

Answer 24

Ah.
\[\Large x= \frac{ -24 \pm 24\sqrt{360} }{ 2 }\]

Answer 25

No, remember 24^2 is under the radical (Don't take it out!)
\[\sqrt{24^2 - 360}\]