Question

help with...4x^2+8x-21=0

Answer 1

do you know the quadratic formula?

Answer 2

no..i don think so?

Answer 3

ok we can try to factor it then

Answer 4

yeah thats what im doing..i have to factor it

Answer 5

a=4, b=8, c=-21
Find factors of a*c that add up to be b

Answer 6

what is a*c?

Answer 7

a*c=-84

Answer 8

right! a*c=-4(21) play with this until you get the sum of the factors to be b=8
-4+21 is not 8
a*c=12(-7)
12-7 is not 8
a*c=6(-14)
is 6-14 =8?

Answer 9

-8 yeah

Answer 10

but we want 8
how can we get 8

Answer 11

what if you said a*c=-6(14)
what is the sum of those two factors?

Answer 12

...8!

Answer 13

right!

Answer 14

now replace the bx term with what you just found but you need an x behind each term so it equals bx

Answer 15

4x^2+14x-6x-21=0

Answer 16

ohhh okay then you have to group it right?

Answer 17

right!

Answer 18

so then it would be(4x^2+14x)(-6x-21)=0 which then what?

Answer 19

no!

Answer 20

what??

Answer 21

what do 4x^2 and 14x have in common?____________
what do -6x and -21 have in common?___________

Answer 22

4x
? idk

Answer 23

2x
-3
so the first 2 terms we factor out 2x(2x+7)
so the second 2 terms we factor out -3(2x+7)
so 4x^2+14x-6x-21=2x(2x+7)-3(2x+7)
can we do anything else?

Answer 24

you still there?

Answer 25

we are almost there

Answer 26

yeha ohh aha i would have never thought of that..

Answer 27

then you do 2x-3=0 and 2x+7=0..

Answer 28

there is 2x+7 in both of those two terms above so we can factor a 2x+7 out of both giving us
(2x+7)(2x-3)
this expression was orignally set =0
so we have (2x+7)(2x-3)=0
so either 2x+7=0 or 2x-3=0
when i say both its the exclusive kind

Answer 29

right

Answer 30

you got that part?
was the factoring the problem you were having?

Answer 31

then the answer is x=2/3 and x=2/7!!

Answer 32

omg thanks soo much for your help!! haha sorry that took me forever to figure out:/ thanks though!

Answer 33

x=2/3 is right but x=-7/2 for the second one