Question

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

Answer 1

@Hero @dan815 @iambatman

Answer 2

@phi @amistre64

Answer 3

@Nnesha mind helping :D

Answer 4

not to much this time...

Answer 5

@Nnesha

Answer 6

First, make the coefficient of the x^2 term 1 by dividing both sides by 4.

Answer 7

ok

Answer 8

so 4 by which sides?

Answer 9

Divide all terms on both sides of the equation by 4.

Answer 10

the x^2 and the 8x by 4?

Answer 11

Everything, yes. What will it look like?

Answer 12

uh... well 8x would be 2x?

Answer 13

Yup. Keep going.

Answer 14

and what about the ^2

Answer 15

is that 4^2?

Answer 16

Divide 4x^2 by 4. What do you get?\[\frac{ 4x^2 }{ 4 } = ?\]

Answer 17

just x^2?

Answer 18

Right. Keep going.

Answer 19

1 divided by 4 is that 4?

Answer 20

No. It's \(\frac{1}{4}\). What about the right hand side? Gotta do that too.

Answer 21

0

Answer 22

Good. So, dividing everything by 4 gives\[x^2 + 2x + \frac{ 1 }{ 4 } = 0\]OK so far?

Answer 23

alright

Answer 24

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?

Answer 25

uh - 1/4?

Answer 26

thats a negative

Answer 27

OK. What does the whole equation look like now?

Answer 28

x^2 + 2x - 1/4?

Answer 29

Not quite. What happened to the equals sign?

Answer 30

idk is it x^2 + 2x - 1/4 =0
or
x^2 + 2x = 1/4?

Answer 31

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?

Answer 32

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

Answer 33

This is not an equation. What happened to the equal sign. It can't just disappear.

Answer 34

you dont have one you used it when you crossed out the 1/4ths

Answer 35

thats how i was tought...

Answer 36

Sorry, no. Equals signs don't disappear. What you are left with is\[x^2 + 2x = -\frac{ 1 }{ 4 }\]Do you understand?

Answer 37

ooo ok

Answer 38

OK. So now you're ready to complete the square on the left hand side. Do you remember how to do it?

Answer 39

some more dividing? lawl

Answer 40

Not really :) Do you know how to complete the square?

Answer 41

mm take half the sq on both sides?

Answer 42

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?

Answer 43

your left with x +2? after taking away one x from each of the sides?

Answer 44

No. What is the coefficient of the 'x' term on the left hand side?

Answer 45

sorry idk that..

Answer 46

What number is multiplying x on the left hand side?

Answer 47

1

Answer 48

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?

Answer 49

omg i said idk geez...