Hey can someone please help me out with this? I'll fan and medal :)
Write x^2 - 2x - 3 = 0 in the form (x - a)^2 = b, where a and b are integers.
(x - 4)^2 = 3
(x - 3)^2 = 2
(x - 2)^2 = 1
(x - 1)^2 = 4

- anonymous

- schrodinger

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- anonymous

complete the square

- anonymous

do you know how to do that?

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## More answers

- anonymous

Umm, kind of. Could you help walk me through it?

- anonymous

sure

- anonymous

Ok, so I'm not sure where to start...

- anonymous

sorry about that

- anonymous

first step is to move the -3 to the other side of the equation

- anonymous

No problem :)

- anonymous

so add 3 to both sides to get
x^2 - 2x = 3

- anonymous

Ok, so it would read x^2 - 2x = 3?

- anonymous

Oh, wait that's what you put lol

- anonymous

that's right

- anonymous

Ok, and then I might try to factor?

- anonymous

|dw:1433358733396:dw|

- anonymous

now divide the -2x by -2

- anonymous

this gives you 1

- anonymous

|dw:1433358802037:dw|

- anonymous

then you square 1 and put it back into the equation

- anonymous

which gives

- anonymous

|dw:1433358865720:dw|

- anonymous

Wait, I think I got lost somewhere. So after you divide the -2x by -2, you have to divide the other side of the equation by -2 which gives you the equation x^2 - x = -1.5. Right?

- anonymous

no, not when completing the square. we are only looking at the right side of the equation right now

- anonymous

sorry, i meant the left side of the equation

- anonymous

Hmmm, I'm still lost.

- anonymous

all we are doing is adding a number to the left side of the equation so we get a factor for x with multiplicity 2

- anonymous

we then add that same number to the right side of the equation

- anonymous

i think you will understand it when I go through all the steps

- anonymous

so we added 1 to x^2 - 2x on the left side of the equation.
since we added 1 to one side of the equation, we now add 1 to the other side

- anonymous

Ok, so now the equation is x^2 + 1 = 4

- anonymous

|dw:1433359235489:dw|

- anonymous

the -2x is still there

- anonymous

Wait I meant x^2 -2x + 1 = 4

- anonymous

Yeah :)

- anonymous

thats right, now factor x^2-2x+1

- anonymous

I think this is where I get lost

- anonymous

I know how to factor but this one is different lol I guess

- anonymous

ok, what two numbers multiply together to get 1

- anonymous

1 and 1

- anonymous

add them together

- anonymous

2 :)

- anonymous

its suppose to add to -2 so 1 and 1 doesn't work.

- anonymous

Oh, ok so it would have to be -1 and -1

- anonymous

what other 2 numbers multiply together to get 1

- anonymous

that's right

- anonymous

so what does the equation look like factored?

- anonymous

Oh, I think I got it (maybe)! Is it (x - 1)^2 = 4?

- anonymous

good job! :)

- anonymous

Yay! Thank you so much @10115658 It makes perfect sense now. :) I am now officially a fan ;)

- anonymous

awesome

- anonymous

Tttyl and thanks again :)

- anonymous

*ttyl

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