some.random.cool.kid
  • some.random.cool.kid
Solve the equation 4x2 + 8x + 1 = 0 by completing the square.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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some.random.cool.kid
  • some.random.cool.kid
@Hero @dan815 @iambatman
some.random.cool.kid
  • some.random.cool.kid
@phi @amistre64
some.random.cool.kid
  • some.random.cool.kid
@Nnesha mind helping :D

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More answers

some.random.cool.kid
  • some.random.cool.kid
not to much this time...
some.random.cool.kid
  • some.random.cool.kid
@Nnesha
anonymous
  • anonymous
First, make the coefficient of the x^2 term 1 by dividing both sides by 4.
some.random.cool.kid
  • some.random.cool.kid
ok
some.random.cool.kid
  • some.random.cool.kid
so 4 by which sides?
anonymous
  • anonymous
Divide all terms on both sides of the equation by 4.
some.random.cool.kid
  • some.random.cool.kid
the x^2 and the 8x by 4?
anonymous
  • anonymous
Everything, yes. What will it look like?
some.random.cool.kid
  • some.random.cool.kid
uh... well 8x would be 2x?
anonymous
  • anonymous
Yup. Keep going.
some.random.cool.kid
  • some.random.cool.kid
and what about the ^2
some.random.cool.kid
  • some.random.cool.kid
is that 4^2?
anonymous
  • anonymous
Divide 4x^2 by 4. What do you get?\[\frac{ 4x^2 }{ 4 } = ?\]
some.random.cool.kid
  • some.random.cool.kid
just x^2?
anonymous
  • anonymous
Right. Keep going.
some.random.cool.kid
  • some.random.cool.kid
1 divided by 4 is that 4?
anonymous
  • anonymous
No. It's \(\frac{1}{4}\). What about the right hand side? Gotta do that too.
some.random.cool.kid
  • some.random.cool.kid
0
anonymous
  • anonymous
Good. So, dividing everything by 4 gives\[x^2 + 2x + \frac{ 1 }{ 4 } = 0\]OK so far?
some.random.cool.kid
  • some.random.cool.kid
alright
anonymous
  • anonymous
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?
some.random.cool.kid
  • some.random.cool.kid
uh - 1/4?
some.random.cool.kid
  • some.random.cool.kid
thats a negative
anonymous
  • anonymous
OK. What does the whole equation look like now?
some.random.cool.kid
  • some.random.cool.kid
x^2 + 2x - 1/4?
anonymous
  • anonymous
Not quite. What happened to the equals sign?
some.random.cool.kid
  • some.random.cool.kid
idk is it x^2 + 2x - 1/4 =0 or x^2 + 2x = 1/4?
anonymous
  • anonymous
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?
some.random.cool.kid
  • some.random.cool.kid
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
anonymous
  • anonymous
This is not an equation. What happened to the equal sign. It can't just disappear.
some.random.cool.kid
  • some.random.cool.kid
you dont have one you used it when you crossed out the 1/4ths
some.random.cool.kid
  • some.random.cool.kid
thats how i was tought...
anonymous
  • anonymous
Sorry, no. Equals signs don't disappear. What you are left with is\[x^2 + 2x = -\frac{ 1 }{ 4 }\]Do you understand?
some.random.cool.kid
  • some.random.cool.kid
ooo ok
anonymous
  • anonymous
OK. So now you're ready to complete the square on the left hand side. Do you remember how to do it?
some.random.cool.kid
  • some.random.cool.kid
some more dividing? lawl
anonymous
  • anonymous
Not really :) Do you know how to complete the square?
some.random.cool.kid
  • some.random.cool.kid
mm take half the sq on both sides?
anonymous
  • anonymous
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?
some.random.cool.kid
  • some.random.cool.kid
your left with x +2? after taking away one x from each of the sides?
anonymous
  • anonymous
No. What is the coefficient of the 'x' term on the left hand side?
some.random.cool.kid
  • some.random.cool.kid
sorry idk that..
anonymous
  • anonymous
What number is multiplying x on the left hand side?
some.random.cool.kid
  • some.random.cool.kid
1
anonymous
  • anonymous
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?
some.random.cool.kid
  • some.random.cool.kid
omg i said idk geez...
anonymous
  • anonymous
|dw:1443484097406:dw|
anonymous
  • anonymous
In \(2x\), the \(x\) is being multiplied by \(2\). The 2 is called the coefficient of x. Do you understand?
some.random.cool.kid
  • some.random.cool.kid
that is a variable you cant multiply that :/
some.random.cool.kid
  • some.random.cool.kid
you have to simplify it...
anonymous
  • anonymous
Sure you can. 2 times x is 2x. 14 times y is 14y. And so on.
some.random.cool.kid
  • some.random.cool.kid
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
anonymous
  • anonymous
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?
some.random.cool.kid
  • some.random.cool.kid
1
some.random.cool.kid
  • some.random.cool.kid
anyways those are what i have...
some.random.cool.kid
  • some.random.cool.kid
im thinking its bewtween those...
anonymous
  • anonymous
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?
some.random.cool.kid
  • some.random.cool.kid
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
anonymous
  • anonymous
How do you get that?
some.random.cool.kid
  • some.random.cool.kid
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
anonymous
  • anonymous
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.
some.random.cool.kid
  • some.random.cool.kid
this is my work lol
some.random.cool.kid
  • some.random.cool.kid
these were my answers and your answer werent near what i had...
some.random.cool.kid
  • some.random.cool.kid
@Nnesha
anonymous
  • anonymous
You haven't completed the work required to arrive at an answer.
some.random.cool.kid
  • some.random.cool.kid
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
some.random.cool.kid
  • some.random.cool.kid
the variables i mean...

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