[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.89,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.89,0:00:03.59,Default,,0000,0000,0000,,Welcome to part two of\Nthe presentation on
Dialogue: 0,0:00:03.59,0:00:05.66,Default,,0000,0000,0000,,quadratic equations.
Dialogue: 0,0:00:05.66,0:00:08.47,Default,,0000,0000,0000,,Well, I think I thoroughly\Nconfused you the last time
Dialogue: 0,0:00:08.47,0:00:11.17,Default,,0000,0000,0000,,around, so let me see if I\Ncan fix that a bit by doing
Dialogue: 0,0:00:11.17,0:00:12.77,Default,,0000,0000,0000,,several more examples.
Dialogue: 0,0:00:12.77,0:00:15.43,Default,,0000,0000,0000,,So let's just start with\Na review of what the
Dialogue: 0,0:00:15.43,0:00:16.38,Default,,0000,0000,0000,,quadratic equation is.
Dialogue: 0,0:00:16.38,0:00:19.65,Default,,0000,0000,0000,,The quadratic equation says, if\NI'm trying to solve the
Dialogue: 0,0:00:19.65,0:00:31.59,Default,,0000,0000,0000,,equation Ax squared plus Bx\Nplus C equals 0, then the
Dialogue: 0,0:00:31.59,0:00:35.44,Default,,0000,0000,0000,,solution or the solutions\Nbecause there's usually two
Dialogue: 0,0:00:35.44,0:00:38.97,Default,,0000,0000,0000,,times that it intersects the\Nx-axis, or two solutions for
Dialogue: 0,0:00:38.97,0:00:47.61,Default,,0000,0000,0000,,this equation is x equals minus\NB plus or minus the square root
Dialogue: 0,0:00:47.61,0:00:56.39,Default,,0000,0000,0000,,of B squared minus\N4 times A times C.
Dialogue: 0,0:00:56.39,0:01:00.27,Default,,0000,0000,0000,,And all of that over 2A.
Dialogue: 0,0:01:00.27,0:01:02.04,Default,,0000,0000,0000,,So let's do a problem and\Nhopefully this should make
Dialogue: 0,0:01:02.04,0:01:02.69,Default,,0000,0000,0000,,a little more sense.
Dialogue: 0,0:01:02.69,0:01:04.62,Default,,0000,0000,0000,,That's a 2 on the bottom.
Dialogue: 0,0:01:04.62,0:01:13.89,Default,,0000,0000,0000,,So let's say I had the equation\Nminus 9x squared minus
Dialogue: 0,0:01:13.89,0:01:19.95,Default,,0000,0000,0000,,9x plus 6 equals 0.
Dialogue: 0,0:01:19.95,0:01:22.23,Default,,0000,0000,0000,,So in this example what's A?
Dialogue: 0,0:01:22.23,0:01:25.41,Default,,0000,0000,0000,,Well, A is the coefficient\Non the x squared term.
Dialogue: 0,0:01:25.41,0:01:29.82,Default,,0000,0000,0000,,The x squared term is here,\Nthe coefficient is minus 9.
Dialogue: 0,0:01:29.82,0:01:30.62,Default,,0000,0000,0000,,So let's write that.
Dialogue: 0,0:01:30.62,0:01:34.12,Default,,0000,0000,0000,,A equals minus 9.
Dialogue: 0,0:01:34.12,0:01:35.40,Default,,0000,0000,0000,,What does B equal?
Dialogue: 0,0:01:35.40,0:01:39.18,Default,,0000,0000,0000,,B is the coefficient on the x\Nterm, so that's this term here.
Dialogue: 0,0:01:39.18,0:01:43.22,Default,,0000,0000,0000,,So B is also equal to minus 9.
Dialogue: 0,0:01:43.22,0:01:47.14,Default,,0000,0000,0000,,And C is the constant term,\Nwhich in this example is 6.
Dialogue: 0,0:01:47.14,0:01:49.55,Default,,0000,0000,0000,,So C is equal to 6.
Dialogue: 0,0:01:49.55,0:01:52.07,Default,,0000,0000,0000,,Now we just substitute these\Nvalues into the actual
Dialogue: 0,0:01:52.07,0:01:53.26,Default,,0000,0000,0000,,quadratic equation.
Dialogue: 0,0:01:53.26,0:01:59.60,Default,,0000,0000,0000,,So negative B, so it's\Nnegative times negative 9.
Dialogue: 0,0:01:59.60,0:02:00.78,Default,,0000,0000,0000,,That's B.
Dialogue: 0,0:02:00.78,0:02:08.11,Default,,0000,0000,0000,,Plus or minus the square root\Nof B squared, so that's 81.
Dialogue: 0,0:02:08.11,0:02:08.39,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:02:08.39,0:02:10.03,Default,,0000,0000,0000,,Negative 9 squared.
Dialogue: 0,0:02:10.03,0:02:14.72,Default,,0000,0000,0000,,Minus 4 times negative 9.
Dialogue: 0,0:02:14.72,0:02:16.14,Default,,0000,0000,0000,,That's A.
Dialogue: 0,0:02:16.14,0:02:19.48,Default,,0000,0000,0000,,Times C, which is 6.
Dialogue: 0,0:02:19.48,0:02:23.95,Default,,0000,0000,0000,,And all of that over 2\Ntimes negative 9, which
Dialogue: 0,0:02:23.95,0:02:25.63,Default,,0000,0000,0000,,is minus 18, right?
Dialogue: 0,0:02:25.63,0:02:26.72,Default,,0000,0000,0000,,2 times negative 9-- 2A.
Dialogue: 0,0:02:26.72,0:02:29.23,Default,,0000,0000,0000,,
Dialogue: 0,0:02:29.23,0:02:33.76,Default,,0000,0000,0000,,Let's try to simplify\Nthis up here.
Dialogue: 0,0:02:33.76,0:02:37.93,Default,,0000,0000,0000,,Well, negative negative\N9, that's positive 9.
Dialogue: 0,0:02:37.93,0:02:46.48,Default,,0000,0000,0000,,Plus or minus the\Nsquare root of 81.
Dialogue: 0,0:02:46.48,0:02:47.90,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:02:47.90,0:02:50.27,Default,,0000,0000,0000,,This is negative 4\Ntimes negative 9.
Dialogue: 0,0:02:50.27,0:02:53.47,Default,,0000,0000,0000,,Negative 4 times negative\N9 is positive 36.
Dialogue: 0,0:02:53.47,0:02:58.31,Default,,0000,0000,0000,,And then positive 36\Ntimes 6 is-- let's see.
Dialogue: 0,0:02:58.31,0:03:01.33,Default,,0000,0000,0000,,30 times 6 is 180.
Dialogue: 0,0:03:01.33,0:03:07.89,Default,,0000,0000,0000,,And then 180 plus\Nanother 36 is 216.
Dialogue: 0,0:03:07.89,0:03:10.98,Default,,0000,0000,0000,,Plus 216, is that right?
Dialogue: 0,0:03:10.98,0:03:14.49,Default,,0000,0000,0000,,180 plus 36 is 216.
Dialogue: 0,0:03:14.49,0:03:16.84,Default,,0000,0000,0000,,All of that over 2A.
Dialogue: 0,0:03:16.84,0:03:19.57,Default,,0000,0000,0000,,2A we already said is minus 19.
Dialogue: 0,0:03:19.57,0:03:20.74,Default,,0000,0000,0000,,So we simplify that more.
Dialogue: 0,0:03:20.74,0:03:28.09,Default,,0000,0000,0000,,That's 9 plus or minus the\Nsquare root 81 plus 216.
Dialogue: 0,0:03:28.09,0:03:30.40,Default,,0000,0000,0000,,That's 80 plus 217.
Dialogue: 0,0:03:30.40,0:03:38.04,Default,,0000,0000,0000,,That's 297.
Dialogue: 0,0:03:38.04,0:03:41.90,Default,,0000,0000,0000,,And all of that over minus 18.
Dialogue: 0,0:03:41.90,0:03:45.02,Default,,0000,0000,0000,,Now, this is actually-- the\Nhardest part with the quadratic
Dialogue: 0,0:03:45.02,0:03:47.72,Default,,0000,0000,0000,,equation is oftentimes just\Nsimplifying this expression.
Dialogue: 0,0:03:47.72,0:03:50.86,Default,,0000,0000,0000,,We have to figure out if we\Ncan simplify this radical.
Dialogue: 0,0:03:50.86,0:03:53.09,Default,,0000,0000,0000,,Well, let's see.
Dialogue: 0,0:03:53.09,0:03:56.49,Default,,0000,0000,0000,,One way to figure out if a\Nnumber is divisible by 9 is to
Dialogue: 0,0:03:56.49,0:03:58.32,Default,,0000,0000,0000,,actually add up the digits\Nand see if the digits
Dialogue: 0,0:03:58.32,0:03:59.26,Default,,0000,0000,0000,,are divisible by 9.
Dialogue: 0,0:03:59.26,0:03:59.95,Default,,0000,0000,0000,,In this case, it is.
Dialogue: 0,0:03:59.95,0:04:02.51,Default,,0000,0000,0000,,2 plus 9 plus 7 is equal to 18.
Dialogue: 0,0:04:02.51,0:04:04.60,Default,,0000,0000,0000,,So let's see how many\Ntimes 9 goes into that.
Dialogue: 0,0:04:04.60,0:04:07.15,Default,,0000,0000,0000,,I'll do it on the side here; I\Ndon't want to be too messy.
Dialogue: 0,0:04:07.15,0:04:09.45,Default,,0000,0000,0000,,9 goes into 2 97.
Dialogue: 0,0:04:09.45,0:04:13.63,Default,,0000,0000,0000,,
Dialogue: 0,0:04:13.63,0:04:16.19,Default,,0000,0000,0000,,3 times 27.
Dialogue: 0,0:04:16.19,0:04:19.04,Default,,0000,0000,0000,,27-- it goes 33 times, right?
Dialogue: 0,0:04:19.04,0:04:24.29,Default,,0000,0000,0000,,So this is the same thing as 9\Nplus or minus the square root
Dialogue: 0,0:04:24.29,0:04:31.11,Default,,0000,0000,0000,,of 9 times 33 over minus 18.
Dialogue: 0,0:04:31.11,0:04:32.47,Default,,0000,0000,0000,,And 9 is a perfect square.
Dialogue: 0,0:04:32.47,0:04:34.65,Default,,0000,0000,0000,,That's why I actually wanted to\Nsee if 9 would work because
Dialogue: 0,0:04:34.65,0:04:36.39,Default,,0000,0000,0000,,that's the only way I could get\Nit out of the radical, if
Dialogue: 0,0:04:36.39,0:04:37.39,Default,,0000,0000,0000,,it's a perfect square.
Dialogue: 0,0:04:37.39,0:04:40.41,Default,,0000,0000,0000,,As you learned in that exponent\Nrules number one module.
Dialogue: 0,0:04:40.41,0:04:46.14,Default,,0000,0000,0000,,So this is equal to 9 plus\Nor minus 3 times the square
Dialogue: 0,0:04:46.14,0:04:53.23,Default,,0000,0000,0000,,root of 33, and all of\Nthat over minus 18.
Dialogue: 0,0:04:53.23,0:04:54.57,Default,,0000,0000,0000,,We're almost done.
Dialogue: 0,0:04:54.57,0:04:57.84,Default,,0000,0000,0000,,We can actually simplify it\Nbecause 9, 3, and minus 18
Dialogue: 0,0:04:57.84,0:05:00.65,Default,,0000,0000,0000,,are all divisible by 3.
Dialogue: 0,0:05:00.65,0:05:02.27,Default,,0000,0000,0000,,Let's divide everything by 3.
Dialogue: 0,0:05:02.27,0:05:14.37,Default,,0000,0000,0000,,3 plus or minus the square\Nroot of 33 over minus 6.
Dialogue: 0,0:05:14.37,0:05:15.61,Default,,0000,0000,0000,,And we are done.
Dialogue: 0,0:05:15.61,0:05:17.01,Default,,0000,0000,0000,,So as you see, the hardest\Nthing with the quadratic
Dialogue: 0,0:05:17.01,0:05:20.11,Default,,0000,0000,0000,,equation is often just\Nsimplifying the expression.
Dialogue: 0,0:05:20.11,0:05:22.75,Default,,0000,0000,0000,,But what we've said, I know you\Nmight have lost track-- we did
Dialogue: 0,0:05:22.75,0:05:27.12,Default,,0000,0000,0000,,all this math-- is we said,\Nthis equation: minus 9x
Dialogue: 0,0:05:27.12,0:05:30.55,Default,,0000,0000,0000,,squared minus 9x plus 6.
Dialogue: 0,0:05:30.55,0:05:34.20,Default,,0000,0000,0000,,Now we found two x values that\Nwould satisfy this equation
Dialogue: 0,0:05:34.20,0:05:35.97,Default,,0000,0000,0000,,and make it equal to 0.
Dialogue: 0,0:05:35.97,0:05:39.83,Default,,0000,0000,0000,,One x value is x equals\N3 plus the square root
Dialogue: 0,0:05:39.83,0:05:42.10,Default,,0000,0000,0000,,of 33 over minus 6.
Dialogue: 0,0:05:42.10,0:05:45.86,Default,,0000,0000,0000,,And the second value is\N3 minus the square root
Dialogue: 0,0:05:45.86,0:05:50.16,Default,,0000,0000,0000,,of 33 over minus 6.
Dialogue: 0,0:05:50.16,0:05:52.25,Default,,0000,0000,0000,,And you might want to\Nthink about why we have
Dialogue: 0,0:05:52.25,0:05:53.37,Default,,0000,0000,0000,,that plus or minus.
Dialogue: 0,0:05:53.37,0:05:55.49,Default,,0000,0000,0000,,We have that plus or minus\Nbecause a square root could
Dialogue: 0,0:05:55.49,0:05:59.55,Default,,0000,0000,0000,,actually be a positive\Nor a negative number.
Dialogue: 0,0:05:59.55,0:06:02.18,Default,,0000,0000,0000,,Let's do another problem.
Dialogue: 0,0:06:02.18,0:06:05.89,Default,,0000,0000,0000,,Hopefully this one will\Nbe a little bit simpler.
Dialogue: 0,0:06:05.89,0:06:09.21,Default,,0000,0000,0000,,
Dialogue: 0,0:06:09.21,0:06:16.78,Default,,0000,0000,0000,,Let's say I wanted to\Nsolve minus 8x squared
Dialogue: 0,0:06:16.78,0:06:21.00,Default,,0000,0000,0000,,plus 5x plus 9.
Dialogue: 0,0:06:21.00,0:06:23.15,Default,,0000,0000,0000,,Now I'm going to assume that\Nyou've memorized the quadratic
Dialogue: 0,0:06:23.15,0:06:25.31,Default,,0000,0000,0000,,equation because that's\Nsomething you should do.
Dialogue: 0,0:06:25.31,0:06:26.63,Default,,0000,0000,0000,,Or you should write it\Ndown on a piece of paper.
Dialogue: 0,0:06:26.63,0:06:31.63,Default,,0000,0000,0000,,But the quadratic equation is\Nnegative B-- So b is 5, right?
Dialogue: 0,0:06:31.63,0:06:34.16,Default,,0000,0000,0000,,We're trying to solve that\Nequal to 0, so negative B.
Dialogue: 0,0:06:34.16,0:06:39.79,Default,,0000,0000,0000,,So negative 5, plus or minus\Nthe square root of B squared-
Dialogue: 0,0:06:39.79,0:06:44.03,Default,,0000,0000,0000,,that's 5 squared, 25.
Dialogue: 0,0:06:44.03,0:06:50.47,Default,,0000,0000,0000,,Minus 4 times A,\Nwhich is minus 8.
Dialogue: 0,0:06:50.47,0:06:53.82,Default,,0000,0000,0000,,Times C, which is 9.
Dialogue: 0,0:06:53.82,0:06:56.40,Default,,0000,0000,0000,,And all of that over 2 times A.
Dialogue: 0,0:06:56.40,0:07:00.32,Default,,0000,0000,0000,,Well, A is minus 8, so all\Nof that is over minus 16.
Dialogue: 0,0:07:00.32,0:07:04.09,Default,,0000,0000,0000,,So let's simplify this\Nexpression up here.
Dialogue: 0,0:07:04.09,0:07:09.44,Default,,0000,0000,0000,,Well, that's equal to\Nminus 5 plus or minus
Dialogue: 0,0:07:09.44,0:07:13.63,Default,,0000,0000,0000,,the square root of 25.
Dialogue: 0,0:07:13.63,0:07:14.62,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:07:14.62,0:07:18.22,Default,,0000,0000,0000,,4 times 8 is 32 and the\Nnegatives cancel out, so
Dialogue: 0,0:07:18.22,0:07:21.52,Default,,0000,0000,0000,,that's positive 32 times 9.
Dialogue: 0,0:07:21.52,0:07:24.48,Default,,0000,0000,0000,,Positive 32 times 9, let's see.
Dialogue: 0,0:07:24.48,0:07:26.72,Default,,0000,0000,0000,,30 times 9 is 270.
Dialogue: 0,0:07:26.72,0:07:31.11,Default,,0000,0000,0000,,It's 288.
Dialogue: 0,0:07:31.11,0:07:31.57,Default,,0000,0000,0000,,I think.
Dialogue: 0,0:07:31.57,0:07:31.80,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:07:31.80,0:07:36.13,Default,,0000,0000,0000,,
Dialogue: 0,0:07:36.13,0:07:37.49,Default,,0000,0000,0000,,288.
Dialogue: 0,0:07:37.49,0:07:40.59,Default,,0000,0000,0000,,We have all of that\Nover minus 16.
Dialogue: 0,0:07:40.59,0:07:42.56,Default,,0000,0000,0000,,Now simplify it more.
Dialogue: 0,0:07:42.56,0:07:47.76,Default,,0000,0000,0000,,Minus 5 plus or minus the\Nsquare root-- 25 plus
Dialogue: 0,0:07:47.76,0:07:51.34,Default,,0000,0000,0000,,288 is 313 I believe.
Dialogue: 0,0:07:51.34,0:07:56.95,Default,,0000,0000,0000,,
Dialogue: 0,0:07:56.95,0:08:00.23,Default,,0000,0000,0000,,And all of that over minus 16.
Dialogue: 0,0:08:00.23,0:08:03.43,Default,,0000,0000,0000,,And I think, I'm not 100% sure,\Nalthough I'm pretty sure.
Dialogue: 0,0:08:03.43,0:08:04.57,Default,,0000,0000,0000,,I haven't checked it.
Dialogue: 0,0:08:04.57,0:08:10.37,Default,,0000,0000,0000,,That 313 can't be factored\Ninto a product of a perfect
Dialogue: 0,0:08:10.37,0:08:11.69,Default,,0000,0000,0000,,square and another number.
Dialogue: 0,0:08:11.69,0:08:13.67,Default,,0000,0000,0000,,In fact, it actually\Nmight be a prime number.
Dialogue: 0,0:08:13.67,0:08:15.60,Default,,0000,0000,0000,,That's something that you\Nmight want to check out.
Dialogue: 0,0:08:15.60,0:08:18.20,Default,,0000,0000,0000,,So if that is the case and\Nwe've got it in completely
Dialogue: 0,0:08:18.20,0:08:21.84,Default,,0000,0000,0000,,simplified form, and we say\Nthere are two solutions, two
Dialogue: 0,0:08:21.84,0:08:24.94,Default,,0000,0000,0000,,x values that will make\Nthis equation true.
Dialogue: 0,0:08:24.94,0:08:30.75,Default,,0000,0000,0000,,One of them is x is equal\Nto minus 5 plus the square
Dialogue: 0,0:08:30.75,0:08:35.83,Default,,0000,0000,0000,,root of 313 over minus 16.
Dialogue: 0,0:08:35.83,0:08:44.11,Default,,0000,0000,0000,,And the other one is x is equal\Nto minus 5 minus the square
Dialogue: 0,0:08:44.11,0:08:49.66,Default,,0000,0000,0000,,root of 313 over minus 16.
Dialogue: 0,0:08:49.66,0:08:51.76,Default,,0000,0000,0000,,Hopefully those two examples\Nwill give you a good
Dialogue: 0,0:08:51.76,0:08:53.94,Default,,0000,0000,0000,,sense of how to use the\Nquadratic equation.
Dialogue: 0,0:08:53.94,0:08:55.86,Default,,0000,0000,0000,,I might add some more modules.
Dialogue: 0,0:08:55.86,0:08:58.23,Default,,0000,0000,0000,,And then, once you master this,\NI'll actually teach you how to
Dialogue: 0,0:08:58.23,0:09:00.37,Default,,0000,0000,0000,,solve quadratic equations when\Nyou actually get a negative
Dialogue: 0,0:09:00.37,0:09:01.91,Default,,0000,0000,0000,,number under the radical.
Dialogue: 0,0:09:01.91,0:09:03.14,Default,,0000,0000,0000,,Very interesting.
Dialogue: 0,0:09:03.14,0:09:06.76,Default,,0000,0000,0000,,Anyway, I hope you can do the\Nmodule now and maybe I'll add a
Dialogue: 0,0:09:06.76,0:09:10.37,Default,,0000,0000,0000,,few more presentations because\Nthis isn't the easiest module.
Dialogue: 0,0:09:10.37,0:09:11.84,Default,,0000,0000,0000,,But I hope you have fun.
Dialogue: 0,0:09:11.84,0:09:13.14,Default,,0000,0000,0000,,Bye.
Dialogue: 0,0:09:13.14,0:09:13.48,Default,,0000,0000,0000,,