Question

Find the real solutions of the equation.
4(x+1)^2 + 14 (x+1) + 6 =0

Answer 1

if the problem was just 4x^2 + 14x + 6 = 0
what would you do?

Answer 2

Factor?

Answer 3

first is to factor out the GCF then factor :)

Answer 4

Which would be 2?

Answer 5

yes :)

Answer 6

Ok, so 2(2+7+6) This doesn't look right to me. Can you please show me?

Answer 7

4x^2 + 14x + 6 = 0 factor out a 2
2(2x^2 + 7x + 3) = 0 then factor
2(2x+3)(x+2) = 0
understand this so far?

Answer 8

Yes

Answer 9

so instead of x it was (x+1) so you would be getting
2 (2x +3) (x +2) = 0
2*(2(x+1) + 3)*((x+1) + 2) = 0
see?

Answer 10

Yes, I think so

Answer 11

then
2*(2(x+1) + 3)*((x+1) + 2) = 0
2 ( 2x + 2 + 3) ( x + 1 +2) = 0
2 ( 2x + 5 ) ( x + 3 ) = 0

Answer 12

Where did you get the 5 from?

Answer 13

2(x+1) + 3 = 2(x) + 2(1) + 3 = 2x + 2 + 3 = 2x + 5

Answer 14

ok

Answer 15

so solve for x for 2x + 5 = 0 and x + 3 = 0

Answer 16

I am studying for my midterm review, and on the answer sheet it says the answer is (-3/2,-4)

Answer 17

hmm, oh, sorry :/ I made a mistake
2(4(x+1)^2 +7(x+1) + 3) = 0 factors to
2(4(x+1) + 3)((x+1)+1) = 0
but I'm not sure how that is the answer :/ hmmm

Answer 18

I am so confused!

Answer 19

sorry, would you like me to tag some people to help you?

Answer 20

Yes if you could please.

Answer 21

@SolomonZelman @shamil98 @ehuman If you guys aren't too busy

Answer 22

Let me think, hold on...

Answer 23

-7

Answer 24

@hilynn3, more help?

Answer 25

how did you get -7?

Answer 26

I did it in my head, I'll explain....

Answer 27

Let x+1=a
OK?

Answer 28

@60jigglypuff314, do you know how to get to it, or not? b/c I can't stay here unreplied for ever.

Answer 29

@jigglypuff314

Answer 30

if you let (x+1) = x in 4(x+1)^2 + 14(x+1) + 6 = 0
then 4x^2 + 14x + 6 = 0 which you can factor to
(4x+2)(x+3) = 0 then factor out a 2
2(2x+1)(x+3) = 0 then solve for the x's
2x+1 = 0 so 2x = -1 so x = -1/2
x + 3 = 0 so x = -3
and x = (x+1) so
(x+1) = -1/2 so x = -1/2 - 1 = -3/2
(x+1) = -3 so x = -3 -1 = -4
so x = -3/2, -4

Answer 31

4(x+1)^2 + 14 (x+1) + 6 =0

The answer is not -7.

let (x+1) =a just to make it a little easier, so sub a for (x+1)
4a^2+14a+6=0 divide by 2
2a^2+7a+6=0

Can you guys solve it from there?

Answer 32

Solve for a, and x will be EZ!