Welcome to the second part of the show Quadratic equations Well, I think I confused you the last time So let me see if I can fix this a little bit with a solution More examples .. Let’s start with a review to find out Quadratic equation The quadratic equation is, that if I try to solve The equation Ax ^ 2 + Bx + C = 0, so the The solution or solutions, because there are often 2 X the intersection with the x axis, or two solutions For this equation is x = -B + or – square root For B ^ 2 – 4 x A x C All this divided by 2A So let us solve an issue and I hope it should be clarified The idea is yours These are 2 below Let’s assume I have the equation -9x ^ 2 – 9x + 6 = 0 So in this example what is A? Well, A is an x \u200b\u200b^ 2 expression operator The expression x ^ 2 is here, and its parameter is -9 Let’s write that A = -9 How much is B? B is the coefficient of the expression x, so it is this expression here So B is also equal to -9 And C is the constant, which in this example is 6 C = 6 Now we have distributed these values \u200b\u200bover Current quadratic equation -B, bars for negative × -9 Visawi B + Or – the square root of B ^ 2, this equals 81 is not it? -9 ^ 2 – 4 x -9 This is A X C, i.e. 6 And all of that divided by 2 × -9, what It’s 81, right? 2 x -9 –2A Let’s try to simplify it Well, -9, this is positive 9 + Or – the square root of 81 lets see This is -4 x -9 -4 x -9 = positive 36 Then that’s positive 36 x 6 – let’s see 30 x 6 = 180 Then 180 + 36 others = 216 + 216, is it true? 180 + 36 = 216 All this divided by 2A 2A We have said it equals -19 So we simplify that further 9 + or – square root of 81 + 216 This is equal to 80 + 217 It equals 297 And all of that divided by -18 Now, this – that’s the hardest part of The quadratic equation is the simplification of this phrase We have to find out if we can simplify this root Well, let’s see The way to find out if this number is divisible by 9 is that We collect all of his houses and see if the total Divide by 9 In this case it is 2 + 9 + 7 = 18 Let’s see how many by dividing it by 9 I’m going to do it here on this side, I don’t want to make a mess 297 ÷ 9 3 x 27 27 – = 33, right? This is equivalent to 9 + or – square root For 9 x 33 / -18 And 9 full square That is why I wanted to show you if the 9 will succeed because This is the only way I can get it out of the root, then That was a whole square As you heard in the rules of foundations question No. 1 This is equal to 9 + or – 3 x The square root of 33, all of that divided by -18 We almost finished We can simplify it because 9, 3 and -18 They all divide by 3 Let’s divide everything by 3 3 + or – square root of 6/33 And we’re done As you can see, the most difficult thing is The quadratic equation is the simplification of the phrase But what we said, I know you may have lost control – we did With all of these mathematical operations– is we said, this equation: -9x ^ 2 9x + 6- Now we have created two x values \u200b\u200bthat achieve this equation And make it equal to 0 The value of the first x is 3 + square root For 6/33 And the second value is 3 – the square root For 6/33 Perhaps you want to think about why there is The + and – We have the + and – because the square root can To be a positive or negative number Let us solve another issue I hope this issue will be a little simpler Suppose we want to solve -8x ^ 2 + 5x + 9 Now I will assume you are saving Quadratic equation because this is something you must do Or you should write it on paper But the square equation is -B – so b = 5, right? We try to be equal to 0, so -B -5 + or – the square root of B ^ 2 It is 5 ^ 2, and equals 25 – 4 x A, E-8 X C, i.e. 9 And all of that divided by 2 × A Well, A = -8, so all of that is divided by -16 Let’s simplify this phrase here Well, that’s equal to -5 + or – The square root of 25 lets see 4 x 8 = 32 and the negative signals are deleted It becomes 32 x 9 Positive 32 x 9, let’s see 30 x 9 = 270 = 288 I think True? 288 We all have that divided by -16 Now we simplify it more -5 + or – square root – 25 + 288 = 313 And all of that divided by -16 And I think, I am not 100% sure, although I am sure I didn’t check that out 313 cannot be analyzed to be a product Full box and other number In fact, it may be a prime number This is something you might want to check If this is the case we have obtained it In simple terms, we say that there are two solutions Any two values \u200b\u200bof x make this equation correct One of them is x = -5 + Square Root of 313 / -16 The other is x = -5 The square root of 16/313 I hope that these two examples have given you Feeling good to use the Quadratic Equation Maybe I will add more questions Then, when you master it, I will teach you how Solve quadratic equations when you get Negative number under the root very fun In any case, I hope you can solve the example now and maybe I will add More offers because this is not the simplest issue But I hope you enjoyed it Bye .

Algebra