Question

taking the square root and show steps
4x^2+8x+3=0

Answer 1

sounds like you want to complete the square on one side
to solve

Answer 2

\[4x^2+8x=-3 \\ \text{ divide both sides by 4 } \\ x^2+2x=-\frac{3}{4}\]

do you recall how to factor x^2+2x+1?

Answer 3

hint:
\[x^2+2x+1=(x+1)^2 \]

Answer 4

add one on both sides and try to use that last equation I posted

Answer 5

4x^2 + 8x + 4 = 1
(2x+2)^2 = 1
2x+2 = plus or minus 1
x = -1/2 or -3/2
?

Answer 6

seems great!
\[x^2+2x=\frac{-3}{4} \\ x^2+2x+1=\frac{-3}{4}+1 \\ x^2+2x+1=\frac{-3}{4}+\frac{4}{4} \\ (x+1)^2=\frac{1}{4} \\ x+1= \pm \frac{1}{2} \\ x=- 1 \pm \frac{1}{2} =\frac{-2}{2} \pm \frac{1}{2}=\frac{-2 \pm 1}{2} \\ \text{ so } x=\frac{-2+1}{2}=\frac{-1}{2} \text{ or } x=\frac{-2-1}{2}=\frac{-3}{2}\]
your way looks cute too :)

Answer 7

thank you could you help me with completing the square on the same question?

Answer 8

on the same question
you already did that

Answer 9

you wrote 4x^2+8x+4 as (2x+2)^2
(2x+2)^2 is the square of (2x+2)

Answer 10

so taking the square and compting the square is the sam eequation?

Answer 11

I think I'm not sure what you are asking?
you solved the equation above by completing the square..
then you took square root of both sides

Answer 12

so im suppose to show my work for completing the square and taking the root but in that i did both right?

Answer 13

\[(2x+2)^2 =1 \text{ this is what you got after completing the square } \\ \text{ then you took square root of both sides } \\ \sqrt{(2x+2)^2}=\sqrt{1} \\ \sqrt{(2x+2)^2}=1 \ \text{ but this means } 2x+2=\pm 1 \]

Answer 14

so thats the answer for completing the square ?

Answer 15

that is the answer by using the completing the square method

Answer 16

that is the answer you would also get by using any method there is to solve a quadratic such as the quadratic formula or factoring

Answer 17

though it would be a bit tricky to factor the expression on the left hand side since it wouldn't be doable over integers but that doesn't mean it can't be done at all

Answer 18

could i give that whole equation and answer all the questions in one

Answer 19

welll besides the factoring

Answer 20

I don't see how taking the square root and completing the square should have there on separate method
you complete the square then take square root

but anyways quadratic formula is easy you just use:
\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]


factoring 4x^2+8x+3 is actually not tricky (I lied ) 4(3)=6(2) and 6+2=8

Answer 21

\[4x^2+8x+3 = 4x^2+6x+2x+3 \text{ factor this by grouping }\]

Answer 22

ur confusing me with all this

Answer 23

but in either method you use you should get the solutions:
x=-1/2 or x=-3/2

Answer 24

with the use of quadratic formula or factoring?

Answer 25

both. ur talking about factoring rn or

Answer 26

what is rn?

Answer 27

right now

Answer 28

I was talking about both quadratic formula and factoring above:

Answer 29

\[ax^2+bx+c=0 \text{ gives } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \text{ is quadratic formula }\]
you never seen this formula before?

Answer 30

no i have but im not sure how it works

Answer 31

can you compare:
ax^2+bx+c=0
to
4x^2+8x+3=0
and identify a,b, and c?

Answer 32

my math program is super confusing and dosnt explain why it is

Answer 33

no i just need to answer these question