Question

What are the solutions of x2 + 2x − 24 = 0?

Answer 1

have you tried to factor it?

Answer 2

Try to think of FOIL'ing, but in reverse. You are looking for numbers that product to -24, but sum to 2. Once you find those, you still have to set them to equal zero if you want to solve for x.

Answer 3

you can always plug it into the quadratic formula
\[-b \pm \sqrt{(b ^{2}-4ac)}\] all over 2a
a=1
b=2
c=24

Answer 4

thanks but I still don't know the answer

Answer 5

Okay. Well, I would start listing all the factors of 24 (I usually ignore signs at this point and put them back in later). So, start with 1 and 24, then 2 and 12, then 3 and 8, and so on. Doing it that way, even listing factors you are pretty sure aren't the ones you want, often will surprise you when you list the right factors and you instantly know they were the ones you were looking for. Try it.

Answer 6

You have a + sign in front of the middle term, but a - sign in front of the final term. To get that negative sign on the final term, you have to be multiplying a positive number and a negative number. So, can you think of two factors of -24 that add to +2? Here are your choices:

1,-24
2,-12
3,-8
4,-6
6,-4
8,-3
12,-2
24,-1
-1,24
-2,12
-3,8
-4,6
-6,4
-8,3
-12,2
-24,1

When you've made your selection, insert them in the blanks:
x^2+2x -24 = (x ____)(x ____) = 0
and check your work by multiplying it out to make sure you get x^2+2x-24

Because you have a product of two things = 0, you can find the solutions by setting each thing = 0 and solving for x. For example, if your factoring produced
\[(x-1)(x+1) = 0\] you would solve\[x-1=0\]and\[x+1=0\] and find that \(x=1, x=-1\) are your solutions.

Answer 7

Ok thanks so much everyone for help

Answer 8

What did you get for answers?

Answer 9

x = 4, x = −6 is this the correct answer?

Answer 10

That is what I got.

Answer 11

thank you :)