anonymous
  • anonymous
u^2-4u-1=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
What are we doing here?
anonymous
  • anonymous
solving quadratic equations. I just don't know if I need to factor it first
anonymous
  • anonymous
Oh, it won't factor.

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anonymous
  • anonymous
So you can use the quadratic formula or you can solve by completing the square.
anonymous
  • anonymous
can you show me im having a hard time with this math 230 class
anonymous
  • anonymous
You got it! :)
anonymous
  • anonymous
thank you
anonymous
  • anonymous
Now, which way would you like me to show you? By using the quadratic formula, or completing the square?
anonymous
  • anonymous
how about completing the square that seems to be the hardest part
anonymous
  • anonymous
Sure thing!
anonymous
  • 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
  • anonymous
ok
anonymous
  • 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
  • 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
  • anonymous
ok so far so good lol
anonymous
  • anonymous
I left 2 blank spaces for the number we're about to add to both sides.
anonymous
  • anonymous
this was part of what i didnt understand where they got this number from
anonymous
  • 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
  • anonymous
oh yeah i kinda remember doing this before
anonymous
  • 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
  • anonymous
So, we've discovered "good c" is 4 and that'll be the number we fill those blanks in with.
anonymous
  • 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
  • anonymous
ok got it so far
anonymous
  • anonymous
So here's what the left side is factored, and the right side is combined: \[(x-2)^2=5\]
anonymous
  • 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
  • anonymous
Those are your exact answers. If you needed approximate answers, for whatever reason, you could run those through a calculator. :)
anonymous
  • anonymous
Thank you so much you were a lot of help. You made it sound so easy
anonymous
  • anonymous
Did that make sense?
anonymous
  • anonymous
Yay!! :)
anonymous
  • anonymous
yeah a lot more than all the videos i have been watching
anonymous
  • anonymous
Well, I'm happy to help.
anonymous
  • anonymous
I'm going to get a metal, right? ;)
anonymous
  • anonymous
yeah how do i do that new to this site
anonymous
  • anonymous
Perfect! :) Thanks!!
anonymous
  • anonymous
i figured it out lol
anonymous
  • anonymous
one more question though what happens if i can factor it like\[x ^{2}+x+6=0\]
anonymous
  • anonymous
I factored it should i have done that

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