WEBVTT
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Okay, completing the square. We've got X squared
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plus X plus three. Force equal zero. We're
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gonna complete this Our solve this by completing the square
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. So the first thing we do is we subtract
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, um, three force from both sides to get
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the equation in this format. Then we do what's
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called completing the square. We try to turn this
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left. The stars are the expression on the left
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side of this, um, into a perfect square
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. Try no meal. We do that by taking
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half of this value right here. This be value
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the coefficient of the ex term, which is currently
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one. So half of that would be 1/2 and
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then we square it. 1/2 squared is 1/4 so
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we add 1/4 to both sides. The reason we
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do that is because then this try no, me
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over here on the left is a perfect square.
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Try no meal that can be factored like this.
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So, um, X squared plus x plus.
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1/4 is the same as X plus, 1/2 squared
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, and then on the right, we end up
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with, um you know what it is the original
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expression. Wrong. So I'll fix this so I
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could change two months, though. It was supposed
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to be subtraction. So then when we we were
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actually adding three forced to both sides. So there
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we go. So now it's everything's correct. Now
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we can do three force plus one force on the
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right, which is one. Okay. Now,
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the reason we factored was so that we could take
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the square root of both sides and start solving for
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X. So the square root of X plus 1/2
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squares just experts 1/2 the square root of one is
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plus or minus one. And then, um,
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subset of some more room. Here we subtract 1/2
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from both sides and we'll start seeing a picture of
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our answer. Here s O X equals negative 1/2
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plus or minus one. I'm gonna think of one
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as two halfs right here so that I have a
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common denominator and combined these together so negative 1/2 minus
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two halves is negative. Three halfs. That's one
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of our answers. And negative 1/2 plus two halves
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is 1/2. That's our other answer. So these
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are the two solutions to the original equations that we
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found by completing the square