Question

solve by completing the square 4x^2+4x+3=0

Answer 1

so what did you do?

Answer 2

still cannot figure out

Answer 3

Which answer shows these decimals written in order from greatest to least?


76.493 79.2 76.81



A.


79.2 > 76.493 > 76.81


B.


76.81 > 76.493 > 79.2


C.


79.2 > 76.81 > 76.493


D.


76.493 > 79.2 > 76.81

Answer 4

hmmm

Answer 5

first, all terms without x to the other side...

Answer 6

then factor out constant from x^2 term...

Answer 7

\[4x^2+4x+3=0 \Rightarrow 4x^2+4x=-3 \Rightarrow 4(x^2+x+\_)=-3\]blank represents something we have to add to complet the square. at this point we can divide both sides by 4 to simplify...\[\Rightarrow (x^2+x+\_)=-\frac{3 }{ 4 }\]

Answer 8

so for a perfect square trinomial, we get\[\left( x+a \right)=x^2+2ax+a^2\]in your problem, 2a = 1 so a = 1/2. this means that a^2 = (1/2)^2 = 1/4. add this to both sides...\[\Rightarrow (x^2+x+\frac{ 1 }{ 4 })=\frac{ 1 }{ 4 }-\frac{ 3 }{ 4 } \Rightarrow (x^2+x+\frac{ 1 }{ 4 })=-\frac{ 2 }{ 4 }\Rightarrow \left( x+\frac{ 1 }{ 2 } \right)^2=-\frac{ 1 }{ 2 }\]

Answer 9

can you solve from here?

Answer 10

this is confusing

Answer 11

Which answer shows these decimals written in order from greatest to least?


76.493 79.2 76.81



A.


79.2 > 76.493 > 76.81


B.


76.81 > 76.493 > 79.2


C.


79.2 > 76.81 > 76.493


D.


76.493 > 79.2 > 76.81

Answer 12

@pgpilot326

Answer 13

@kaley_loves_backin_lo post in the proper place, not inside another person's post!

Answer 14

ty u for advice umm

Answer 15

okay, you can start by dividing everything by 4...\[4x^2+4x+3=0 \Rightarrow x^2 + x +\frac{ 3 }{ 4 }= 0\]does this make sense?

Answer 16

thanks for your help

Answer 17

yes

Answer 18

okay, then we can move the constant term to the other side...\[x^2+x+\frac{ 3 }{ 4 }=0 \Rightarrow x^2+x=-\frac{ 3 }{ 4 }\]do you follow this?

Answer 19

yes

Answer 20

okay, now we're just gonna look at the left hand side and see what is needed to make it a perfect square. we'll do this with a picture and hopefully this will make it a little clearer...

Answer 21

we want to add to make the rectangle a perfect square. it's gonna be a little trickery because we just want to add a number, nothing involving x.

Answer 22

do you see how it's split up? we're gonna split up the smaller rectangle into 2 equal pieces and rearrange to see what is missing to complete the square.