Solve the equation 4x2 + 8x + 1 = 0 by completing the square.

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Solve the equation 4x2 + 8x + 1 = 0 by completing the square.

Mathematics
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@Nnesha mind helping :D

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Other answers:

not to much this time...
First, make the coefficient of the x^2 term 1 by dividing both sides by 4.
ok
so 4 by which sides?
Divide all terms on both sides of the equation by 4.
the x^2 and the 8x by 4?
Everything, yes. What will it look like?
uh... well 8x would be 2x?
Yup. Keep going.
and what about the ^2
is that 4^2?
Divide 4x^2 by 4. What do you get?\[\frac{ 4x^2 }{ 4 } = ?\]
just x^2?
Right. Keep going.
1 divided by 4 is that 4?
No. It's \(\frac{1}{4}\). What about the right hand side? Gotta do that too.
0
Good. So, dividing everything by 4 gives\[x^2 + 2x + \frac{ 1 }{ 4 } = 0\]OK so far?
alright
Now, we don't want the 1/4 on the left hand side, so subtract 1/4 from both sides. What will it look like then?
uh - 1/4?
thats a negative
OK. What does the whole equation look like now?
x^2 + 2x - 1/4?
Not quite. What happened to the equals sign?
idk is it x^2 + 2x - 1/4 =0 or x^2 + 2x = 1/4?
We better back up a step. You had\[x^2 + 2x + \frac{ 1 }{ 4 } = 0\]To get rid of the 1/4 on the left hand side, you need to subtract it. And the rules of equality say that whatever you do one side of the equation you have to do to the other side as well. So you have to subtract 1/4 from both sides. So\[x^2 + 2x + \frac{ 1 }{ 4 } - \frac{ 1 }{ 4 } = 0-\frac{ 1 }{ 4 }\]Simplify both sides. What will it look like?
wait but if you canceled the other 1/4ths and your left - 1/4 then what is left i dont get it all i se is x^2 + 2x - 1/4
This is not an equation. What happened to the equal sign. It can't just disappear.
you dont have one you used it when you crossed out the 1/4ths
thats how i was tought...
Sorry, no. Equals signs don't disappear. What you are left with is\[x^2 + 2x = -\frac{ 1 }{ 4 }\]Do you understand?
ooo ok
OK. So now you're ready to complete the square on the left hand side. Do you remember how to do it?
some more dividing? lawl
Not really :) Do you know how to complete the square?
mm take half the sq on both sides?
Something like that. You need to add a number to the left hand side that will make it a perfect square trinomial. Look at the coefficient of the 'x' term. Take half of that coefficient and then square it. What number do you get?
your left with x +2? after taking away one x from each of the sides?
No. What is the coefficient of the 'x' term on the left hand side?
sorry idk that..
What number is multiplying x on the left hand side?
1
Oh my. The equation you're working with now is\[x^2 + 2x = -\frac{ 1 }{ 4 }\]The 'x' term on the left hand side is \(2x\). The coefficient is the number that is multiplying the \(x\). What number is it?
omg i said idk geez...
|dw:1443484097406:dw|
In \(2x\), the \(x\) is being multiplied by \(2\). The 2 is called the coefficient of x. Do you understand?
that is a variable you cant multiply that :/
you have to simplify it...
Sure you can. 2 times x is 2x. 14 times y is 14y. And so on.
x equals start fraction three plus or minus square root of six end square root over two end fraction x equals six plus or minus two square root of six end square root x equals start fraction negative two plus or minus square root of three end square root over two end fraction x equals start fraction four plus or minus three square root of six end square root over eight end fraction
So the coefficient of the 'x' term is 2. Now take half of the coefficient - half of 2 is 1. Now square that number. What is 1 squared?
1
anyways those are what i have...
im thinking its bewtween those...
Very good. So you need to add 1 to both sides of the equation\[x^2 + 2x = -\frac{ 1 }{ 4 }\]What will the equation look like?
like this in the end... x equals start fraction four plus or minus three square root of six end square root over eight end fraction
How do you get that?
out of these and based on your thing this was best choice. x equals start fraction three plus or minus square root of six end square root over two end fraction x equals six plus or minus two square root of six end square root x equals start fraction negative two plus or minus square root of three end square root over two end fraction x equals start fraction four plus or minus three square root of six end square root over eight end fraction
If you would like my help in learning how to complete the square, I'll help you. But, if you're just going to copy someone else's work (which hasn't been reduced to lowest terms, by the way), then I'll move on. Good luck with your work.
this is my work lol
these were my answers and your answer werent near what i had...
You haven't completed the work required to arrive at an answer.
the way you were headed i figured i would paste my answers because it seemed like you were going in a different direction... as soon as you said i can multiply i knew it was off because in this course you do not multiply these it strictly says you dont multiply them its supposed to be simplified @ospreytriple
the variables i mean...

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