Question

ok... here's a quadratic equation example... could someone do it and show there work, because no matter how people explain it... I DON"T GET IT.... So here it is... x^2-2x-24=0

Answer 1

the name quadratic, comes from the old days when people used words to describe certain events; in this case the word for "we squared it and got this" was quadratic

Answer 2

4^2 is a quadric

(x-2)^2 is a quadratic

Answer 3

quad means four; and a square has 4 sides .... that sort of logic

Answer 4

what this means to me is; that a quadratic equation can be broken down into 2 baser parts; called factors. and when those factors are multiplied together, we get a product that returns us to the original form

Answer 5

thats the basics as i see them, now how do we apply that to your question?

Answer 6

x^2 -2x -24 = 0 ; thjis tells us that something times something else = 0 for starters

Answer 7

we need to factor, or break the quadratic into its baser parts; turn it into multiplication so that we can determine its behaviour more easily

Answer 8

if a*b = 0; then either a=0 or b=0 right?

Answer 9

a(0) = 0
or
0(b) = 0
or
0*0=0

right?

Answer 10

i think... :/

Answer 11

these are basic concepts that you prolly already know; so what is it specifically that you need help on in order to factor: x^2-2x-24 = 0

Answer 12

i am JUST learning all this in my algebra class which i am almost finished with. The lessons are online and I am having a hard time following it. So I pretty much need to know what steps are involved in solving it. Like what you actually do one your scratch paper, that kind of thing. Thanks!

Answer 13

if it factors nice and pretty like; i mean it doesnt contain square roots and other terrible math notations; the process i use goes like this ... you ready?

Answer 14

step1; factor any common factors out of it; this has none so we can move to the next step

Answer 15

step 2; notice the last number: x^2-2x -24
^^^ this one

it is a negative number which tell me im gonna need to do some subtraction

Answer 16

what you actually write on your paper, assuming these factor, is
\[(x + ?)(x + ??)=0\] and fill the ? spots with two numbers whose product is -24 and whose sum is -2

Answer 17

step 3; notice the middle term: x^2 -2x -24
^^^
its negative which tells me
the larger factor is negative, more
on that soon

Answer 18

step 4; find factors of 24 that subtract to get 2

1,24; 24 - 1 = 23 ... not it

2,12; 12 - 2 = 10 .... not it

4,6 ; 6 - 4 = 2 ..... thats the one

Answer 19

step 5; set up your factors:

(x 6)(x 4)

the larger one is negative as we clued in earlier so...
(x - 6) (x + 4) are our factors

Answer 20

now tell me where you get lost in this :)

Answer 21

Okay, i think I get it... Could I try another one and you could tell me if i get it right? That would rock.

Answer 22

i could, but we are one or two steps away from finishing up this one

Answer 23

oh ok sorrry

Answer 24

once we got factored forms: we solve for our zeroes

(x - 6) (x + 4) = 0 , recall above i stated, that it equals zero when one of the other part is 0

(0) (x+4) = 0

(x-6) (0) = 0

so.....

when does: x-6 = 0
and
when does: x+4 = 0

Answer 25

we get 2 answers for our solution; x = 6 or x=-4 will make our equation equal zero

Answer 26

does that make sense?

Answer 27

yes... :)

Answer 28

good, whats your next question then :)

Answer 29

0 = 6x2 − 10x − 4

Answer 30

same steps; with a twist ....

Answer 31

step 1 is factor out commons; i see at least a 2 that can be factored out, do you?

Answer 32

0 = 2( 3x^2 −5x −2) right?

Answer 33

yes...

Answer 34

step 2; notice the sign for the end, that -2 part; tells us we are going to subtract out factors

step 3; notice the middle term is a -5, the negative tells us the larger factor is going to be negative

Answer 35

step 4; this is the twist, since we got something other than a "1" in front, we multiply it to the end to get something to factor...

3(2) = 6 ; now sort thru the factors of 6 that "subtract" to get 5.

1,6; 6 - 1 = 5 ... thats was nice, first try

Answer 36

step 5; setup up our factors, and the twist is that we have to divide off the front number since we multiplied it in to begin with; we have to "undo" it.

(x 6/3) (x 1/3) ; and the larger "factor" gets the negative

(x - 6/3) (x +1/3) ; and reduce

(x - 2) (x +1/3) ; we can stop here to find the zeroes , do you see why?

Answer 37

step 4 can be generalized in it all, but when the first number is a "1" its kinda pointless; 1(last#) = last#

Answer 38

oh i see... :)

Answer 39

wait actually im confused... now i need to solve for zero right? But how do I do that?

Answer 40

if we want to continue thru to get it "factored" we would go one step further; step 6 :)

2 (x - 2) (x +1/3) ; recall the the denominator came from the front of the equation to begin with, so if there is a denom left after reducing, stick it back in front for a factored form

2 (x - 2) (x +1/3)

2 (x - 2) (3x +1) <--- see what i did?

Answer 41

how do you solve for zero when you are multiplying 2 numbers together? when either number is a zero, the product equals 0 right?

Answer 42

yes... so how do u get a number answer?

Answer 43

(x - 2) * (x +1/3) = 0
=0? =0?

Answer 44

equate both "factors" to equal zero to determine when one or the other equlas zero

this is simply turning it into a "multiplying by zero" effect

Answer 45

5(0) = 0
a(0) = 0
♫(0) = 0

Answer 46

when does x-2 = 0?

when does x+ 1/3 = 0?

Answer 47

so its x-2=0 -> x=2
and
x+1/3=0> x=-1/3 ???

Answer 48

yep; see..

let x = 2 then: (x - 2) * (x +1/3)
(2 - 2) * (2 +1/3)
(0) * (2 +1/3) = 0 right?



let x = -1/3 then: (-1/3 - 2) * (-1/3 +1/3)
(-1/3 - 2) * (0) = 0 right?

Answer 49

ok... that's what i did... YAY! Thank you!!! I really appreciate you helping me!

Answer 50

youre welcome, good luck :)

Answer 51

thanks! :)

Answer 52

i got questions!

Answer 53

use the distributive property to simplify the expression 7(-5x+7)

Answer 54

You should post questions on the math feed from now on... but the anser is...
-35x-7 :)