- Optional filter - |
- Optional filter - |
Hey there guys! Today, I'm going to show all of you how to easily solve any quadratic equation! Yes, thats right! First, you need to know how to get a quadratic problem. Look at this one: X² + 3X + 5 = 0 This is a quadratic problem. Now lets say you have this problem: X² + 3X = 5 Uh oh! This isn't a quadratic anymore! Do not worry. We can easily make it a quadratic, by doing this: X² + 3X + ¯5 = 5 + ¯5 Then it turns into: X² + 3X + 5 = 0 What we did was we had to get a 0 on the right side of the problem. To do so, we had to add 5's opposite which is ¯5. 5 plus ¯5 is 0. But what we do on one side, we must do on the other. So if we add ¯5 on one side, we must add ¯5 on the other side! Then we just work it out. You might be wondering why it came out like "X² + 3X + ¯5 = 0" instead of "X² + ¯2X = 0". The reason is because of the Hippopotamus rule. You can only add "like things" together. Only X²'s can be added to X²'s. X's can only be added to X's, and numbers can only be added to numbers. Try and make these quadratics: X² + 2X = 6 X² - 10X = 12 X² + 4X = 8 Good, now that you know how to convert, lets move on! Here is our Quadratic Formula: X = ¯B ± √B² - 4 • A • C / 2 • A Don't be afraid! It is very easy if you look at it hard enough. Lets look at a quadratic: X² + 3X + ¯5 = 0 I'm going to give each number(X², 3X and ¯5) a name tag. The name tags will be A, B and C. The first number(X²) will be A, the second(3X) is B and the third(¯5) is C. We can now add these to our Quadratic Formula. Lets look at the first part of the Formula: X = ¯B ± This is where we put our B name tag, so instead of writing "X = ¯B ±" we will write just the number, which is now "X = ¯3 ±" See? Lets do the next part: √B² - 4 Instead of writing that, we will write "√3² - 4" So this is what we have so far: X = ¯3 ± √ 3² - 4 Your doing great! Lets continue... Next, we have A • C So instead of writing that, we will write "1 • ¯5" Why did we put 1 instead of X²? Because you ONLY put the numbers. If there is no number by X², then we just put a 1. In fact, X² can also be read as 1X². Anyway, time for our last part! Here we have / 2 • A So we will write "/ 2 • 1 Lets look at our Formula again: X = ¯B ± √ B² - 4 • A • C / 2 • A So instead of that, we will write: X = ¯3 ± √ 3² - 4 • 1 • ¯5 / 2 • 1 Now lets solve it! Lets not worry about the X = ¯3 ± √ part yet. So we have now "3² - 4 • 1 • ¯5" 3² is just like saying "3 • 3", which is 9. So now its: 9 - 4 • 1 • ¯5 In math, we always multiply and divide first. 4 • 1 is 4, and then 4 • ¯5 is ¯20. If you multiply a positive number with a negative, it will be a negative, always. Negative times a negative will be a positive. Anyway, now we have 9 - ¯20, which is 29. If this confuses you, think of negative numbers as subtracting. If you have 5 - 2, the answer is 3. But you can change the 5 - 2 to 5 + ¯ 2, which is still 3. You can change a subtraction problem by instead, adding its opposite. So 9 - ¯20 can be 9 + 20, which is 29. Lets look at our problem so far: X = -3 ± √ 29 / 2 • 1 √ means "The square root of" Here are some examples: √4 is 2 (2 • 2) √9 is 3 (3 • 3) √12 is 4 (4 • 4) It is a number when multiplied by it's self. √25 is 5 (5 • 5) So the square root of 29 is around 5.4(We will round it to 5.4). So now we have: X = ¯3 ± 5.4 / 2 • 1 Lets multiply the last part, making the problem: X = ¯3 ± 5.4 / 2 The / 2 makes it a fraction by the way. All of this is over 2, like ½... So ¯3 ± 5.4 The ± means "plus or minus" You can either add the problem, or subtract it. We have to do both. Lets first add. ¯3 + 5.4 is 2.4, so we now have: X = 2.4 / 2 Now lets subtract! ¯3 - 5.4 is just like saying ¯3 + ¯5.4, which is 8.4. If you add two negative numbers, its the same as adding them. So lets look at our two answers! X = 2.4 / 2 X = ¯8.4 / 2 Congratulations! You just solved your first quadratic! If you need help with any Algebra, just ask, I'll be happy to help! |
 |
19337 - |
|
 |
