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So, but it is still on YouTube that he was going with God.
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Wait, wait, you do?
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Mr. Brian's with me.
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You can still go on the Facebook and just take a link from one of those and that shows all my videos.
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Did you know that there's a love and dislike button now?
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No.
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Okay, so yeah, there are people who are ready.
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Alright, now we go ahead and do this last problem.
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Again, I'm already in there quite very far.
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So, when looking at a problem like this, I've already tested my solution.
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I already know that if this is not factable, I don't see any perfect squares.
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I don't want to complete the square.
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It's just going to be a messy problem anyway, I try to factor it.
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So, my last and final step when I cannot figure out how to factor something,
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I do not see any shortcuts, I'm going to use our lovely quadratic formula.
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Which is opposite of the V, plus or minus, the square root, V squared minus 4 times A times C,
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all over to A.
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Now, from beginning when we were doing quadratic equations, functions, I've always been telling you,
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the first thing I always want you to do is label what your K, B, and CR.
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So, over here I have my A equals 1, B equals 8, and C equals 2.
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And I relate them to the quadratic formula over here.
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Now, all it's simply this, A is not equal to 1.
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Now, all I'm simply going to do is I'm going to evaluate for when A equals 3,
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B equals 8, equals 2 into this formula.
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Therefore, I have a negative A plus or minus the square root of 8 squared minus 4 times 3 times C,
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all over 2 times 3.
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And one last thing I want to mention is, what is this equal?
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What do you get when you do the quadratic formula?
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Well, it's actually what your intercepts are.
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So, now we're solving, this is actually solving for X.
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So, next thing is I'm going to want to actually evaluate what's in my discriminant.
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So, in my evaluate, my discriminant, I have 64 minus 4 times 3, which is 12 times 2 is 24.
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64 minus 20 is given the square root of 40.
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Now, if you remember the discriminant test, whenever you have B squared minus 4 times 8 times C,
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when that is greater than 0, you're going to have real solutions.
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So, therefore, my answer is going to be real.
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Now, if it's a square number, that means if it's 9, 16, 4, 25, 36, 49, 64,
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if it's a square number, then your solutions are going to be rational.
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And if it's not a square number, like square root of 40, you're going to have an irrational real numbers.
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And the last thing is, if I had a B squared minus 4 times 8 times C, less than 0,
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then it's going to be a complex solution.
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That means you're going to have to be negative, because right, you can't take the square root of a negative number.
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And last thing, if B squared minus 4 times 8 times C is equal to 0, or therefore, you're only going to have one real one root.
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Alright, moving away from that.
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So, therefore, now I have X equals negative 8 plus or minus square root of 40 divided by 6.
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So, I'm going to look at this, and I say, can I factor out my square root of 40 at all? And you say, well, I have an additional log you can.
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Because square root of 40 can be broken down into the square root of 4 times 10.
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And why do I break down a square root of 4 times 10? Because 4 is my largest square number that goes into 40.
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And I want square numbers, because when I have a square number, I can actually take the square of that number.
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So, it really helps me out to go and see how to find the square of that number.
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Alright, good. If I have 2 times square root of 10.
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So, now I'm going to rewrite this, X equals negative 8 plus or minus 2 square root of 10 divided by 6.
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And then I notice all of these I can factor out a 2.
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So, when I factor out a 2 out there, I'm going to 3 and it comes in 1 and it comes in negative 4.
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So, X equals a negative 4 plus square root of 10 divided by 3 and X equals a negative 4 minus square root of 10.
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So, those would be my 2 roots.
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So, when you guys can't find a shortcut and you can't factor it, you can always fall back on the quadriple format.
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Just make sure that you simplify your radical as much as possible and use your discriminant test to understand what your answer is going to be.