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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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do you know the quadratic formula?
no..i don think so?
ok we can try to factor it then

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yeah thats what im doing..i have to factor it
a=4, b=8, c=-21 Find factors of a*c that add up to be b
what is a*c?
a*c=-84
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?
-8 yeah
but we want 8 how can we get 8
what if you said a*c=-6(14) what is the sum of those two factors?
...8!
right!
now replace the bx term with what you just found but you need an x behind each term so it equals bx
4x^2+14x-6x-21=0
ohhh okay then you have to group it right?
right!
so then it would be(4x^2+14x)(-6x-21)=0 which then what?
no!
what??
what do 4x^2 and 14x have in common?____________ what do -6x and -21 have in common?___________
4x ? idk
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?
you still there?
we are almost there
yeha ohh aha i would have never thought of that..
then you do 2x-3=0 and 2x+7=0..
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
right
you got that part? was the factoring the problem you were having?
then the answer is x=2/3 and x=2/7!!
omg thanks soo much for your help!! haha sorry that took me forever to figure out:/ thanks though!
x=2/3 is right but x=-7/2 for the second one

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