u^2-4u-1=0

- anonymous

u^2-4u-1=0

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- anonymous

What are we doing here?

- anonymous

solving quadratic equations. I just don't know if I need to factor it first

- anonymous

Oh, it won't factor.

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## More answers

- anonymous

So you can use the quadratic formula or you can solve by completing the square.

- anonymous

can you show me im having a hard time with this math 230 class

- anonymous

You got it! :)

- anonymous

thank you

- anonymous

Now, which way would you like me to show you? By using the quadratic formula, or completing the square?

- anonymous

how about completing the square that seems to be the hardest part

- anonymous

Sure thing!

- anonymous

To get started, we'll write out the formula and identify the pieces:
The first thing to not is that right now it is in standard form.\[u^2-4u-1=0\]
To solve by completing the square, we don't want it in standard form though. The reason we don't want it in standard form is because we're trying to create a perfect square trinomial and our current "c" term does not guarantee we will have a perfect square trinomial. It's the "bad c".

- anonymous

ok

- anonymous

And the "bad c" needs to be moved to the other side of the equation. So we'll add 1 to both sides of this equation:
\[u^2-4u=1\]

- anonymous

Now, I'm going to do a rewrite, but I want to leave room for the "good c" that we're about to create. So here's what it looks like now:
u^2-4u+___=1+___

- anonymous

ok so far so good lol

- anonymous

I left 2 blank spaces for the number we're about to add to both sides.

- anonymous

this was part of what i didnt understand where they got this number from

- anonymous

Now, to find "good c" we take our b value, chop it in half, and square it. Like this:
\[(\frac {b}{2})^2\]

- anonymous

oh yeah i kinda remember doing this before

- anonymous

\[c=(\frac{b}{2})^2\]Now, we'll plug in our 'b' value:
\[c=(\frac{(-4)}{2})^2\]
\[c=(-2)^2\]
c=4

- anonymous

So, we've discovered "good c" is 4 and that'll be the number we fill those blanks in with.

- anonymous

So here's what we have so far:
\[u^2-4u+4=1+4\]Now, we want to factor the left side and combine terms on the right side.

- anonymous

ok got it so far

- anonymous

So here's what the left side is factored, and the right side is combined:
\[(x-2)^2=5\]

- anonymous

From here, we solve using the square root method:
\[\sqrt{(x-2)^2}=\sqrt{5}\]And when we square root both sides of an equation, we need to consider the plus or minus.
\[(x-2)=\pm \sqrt{5}\]Then we add 2 to both sides, and when we write our final answer the plus/minus piece comes second. Like this:
\[x=2\pm \sqrt{5}\]

- anonymous

Those are your exact answers. If you needed approximate answers, for whatever reason, you could run those through a calculator. :)

- anonymous

Thank you so much you were a lot of help. You made it sound so easy

- anonymous

Did that make sense?

- anonymous

Yay!! :)

- anonymous

yeah a lot more than all the videos i have been watching

- anonymous

Well, I'm happy to help.

- anonymous

I'm going to get a metal, right? ;)

- anonymous

yeah how do i do that new to this site

- anonymous

Perfect! :) Thanks!!

- anonymous

i figured it out lol

- anonymous

one more question though what happens if i can factor it like\[x ^{2}+x+6=0\]

- anonymous

I factored it should i have done that

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