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Okay. Completing the square. This gets a little
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bit tricky. They get tougher than this even.
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But try and walk you through this here stuff by
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step. I have already completed this problem, and
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I have checked my answer already. So do you
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know it's right. Here we go. So the
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first thing I gotta do is add seven double sides
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of this to solve by completing the square, Um
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, and I've got to give the X squared and
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the ex term alone in the left. So added
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seven to both sides. Now I'm going to divide
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everything by five because I want my lead coefficient to
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be one. Okay, so now that I've got
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the lead coefficient one, I can actually complete the
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square. So the process of completing the square is
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the idea of taking half the be value. You
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can only do this with legal officials. 1/2 of
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two is one. And then you square it once
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where this one So I'm gonna add one to both
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sides of this equation. There are adding one to
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both sides. The question The only reason I did
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5 50 because I wanted a common denominator. Okay
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, So why did I have one? Because now
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I've got a perfect square trying no meal over here
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. And they left expert plus two x plus one
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, which could be factored easily as X plus one
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squared on the right. I'll just simplify. 7/5
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um, plus 5/5 is 12 5th The reason I
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wanted affected that, like that is so I could
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turn it into X S O. I could take
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the square root of both sides. All right.
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The square root of, um, expose one squared
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is just explosive. One in the square root of
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12 5th is plus or minus squared of 12 5th
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Then I can I subtract one from both sides and
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I get kind of my answer. All right,
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so, um, negative one plus or minus the
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square to 12 5th Usually we don't leave fractions.
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Insider radicals, though that's not considered simplified. There's
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an easy fix, though. If if you just
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multiplied by the square to five over the square to
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five, that'll be that'll rationalize that, Um,
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the denominator it's called and I'll give us this new
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expression negative one plus or minus the square root of
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60 over five. Because on the bottom. You
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get squared five times, escorted five, which is
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five and scored 12 times scored. Five is the
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12 squirt of 60. But I would even go
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further with this, and I would simplify that radical
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in the numerator sixties, divisible by perfect square,
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which is four four times fifteen's too square to 60
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and square to forest too. So two times the
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square of 15 is equal to the square to 60
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and ever five. So you have to ask your
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teacher what they're looking for out of you right now
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. But technically, this is the simplified answer.
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Negative one plus or minus two times the square of
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15 all over five. They might just want you
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to go with this for now because I know you
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are in just chapter one of this book, so
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not sure how difficult don't want to make it.
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But technically, that's the simplified answer