Solve for x, X^2+6x-40=0

Question

anonymous · Answer

You can either factor or use the quadratic formula.

anonymous · Answer

I am not quite sure how to do that.

anonymous · Answer

This one is factorable, so lets do that.

anonymous · Answer

Because it is an x^2 with no number multiplied by it, we know it will be in the form (x+?)(x+?)

anonymous · Answer

Have you done FOIL yet?

anonymous · Answer

No I have no idea what that is

anonymous · Answer

If we have something like this (x-4)(x+3) you can expand it by using a method called FOIL.

anonymous · Answer

First
Outside
Inside
Last

anonymous · Answer

you multiply the terms like that and add them together

anonymous · Answer

in this example, we would end up with x^2 +3x -4x -12

anonymous · Answer

which simplifies to x^2 -x -12

anonymous · Answer

Now, notice that that looks a whole lot like the problem you started with!  We are going to do FOIL backwards.

anonymous · Answer

X^2+6x-40
we are looking for two numbers that when multiplied give us -40, but when added give us 6.

anonymous · Answer

they can be positive or negative, and they'll be integers in a basic problem such as this.  Any numbers come to mind?

anonymous · Answer

How about 4 and -10?

anonymous · Answer

So, we end up with this:
(x+4)(x-10)
When FOILed, we get this:
X^2+6x-40

Remember, this is set equal to zero so we have ended up with (x+4)(x-10)=0

anonymous · Answer

Now we can solve it.
This equals zero when x is either -4 or 10.

anonymous · Answer

This is how I got that:
you can set both parts equal to zero:
x-4=0
x+10=0
solving, we get x to equal -4 and 10.

anonymous · Answer

oops, i meant this:

This is how I got that: 
you can set both parts equal to zero: 
x+4=0 
x-10=0 
solving, we get x to equal -4 and 10.

Quadratic equations like these have two answers the majority of the time, so the answer would be x=-4, 10

anonymous · Answer

err, scratch that

anonymous · Answer

Back when I first said "How about 4 and -10?" I got the signs backwards.  So x actually comes out to equal 4 and -10 in the end...
sorry

anonymous · Answer

Did you get all that?  Kinda confusing the first time around...

anonymous · Answer

It's fine. Thank you for your help! I really appreciate it. I kind of understand. Im pretty bad at math.