In this video, we're going to talk about how to solve quadratic equations using the quadratic formula. So let's start with this one. Let's say we have the equation 2x squared plus 3x minus 2 is equal to 0. And our goal is to solve for x.
We want to calculate the value of x that makes this equation true. So here is the quadratic formula that we need to use. It's negative b plus or minus the square root of b squared minus 4ac divided by 2a. Now we need to know what a, b, and c are equal to. So in this format, where you have all of the x variables to the left and 0 on the right, a is the number in front of x squared, b is the number in front of x, and c is the constant term.
So this is going to be, I'm going to rewrite it here, x is equal to negative b, b is positive 3, plus or minus the square root of b squared, so that's 3 squared minus 4 times a, a is 2, times c, which is negative 2, all divided by 2a, or 2 times 2. So we have negative 3 plus or minus the square root, 3 squared is 9, negative 4 times 2 is negative 8, and negative 8 times negative 2 is positive 16. On the bottom, we have 2 times 2, which is 4. Now, 9 plus 16 is 25. And the square root of 25 is 5. So right now, that's what we have. Notice the plus and minus symbol. So we need to break this up into two parts.
So we're going to have negative 3 plus 5 divided by 4, and negative 3 minus 5 divided by 4. Negative 3 plus 5 is positive 2. Negative 3 minus 5 is negative 8. So right now, we have two different answers. Now, we can reduce 2 over 4 to 1 over 2, if you divide both numbers by 2. And 8 divided by 4 is negative 2. So x... can equal one half or x can equal negative two. And so that's how you can solve a quadratic equation using the quadratic formula. Now if you want to check your answer, you can plug it in.
Let's plug in negative 2 into this equation. So we have 2 times negative 2 squared plus 3 times minus 2 minus 2. Let's see if that equals 0. Negative 2 squared is negative 2 times negative 2, which is 4. 3 times negative 2 is negative 6. Now, 2 times 4 is 8. Negative 6 minus 2 is negative 8. 8 minus 8 is 0. So we know that this answer works. And you could try the other one too.
That's going to work as well. But now let's move on to our next example. Let's say we have... this particular quadratic equation.
Go ahead and use the quadratic formula to get the answer. So we can see that a is 6, b is negative 17, and c is 12. So let's begin by writing the formula. So it's x is equal to negative b plus or minus the square root of b squared minus 4ac divided by 2a.
So b is negative 17. And then we have b squared, that's negative 17 squared, minus 4. a is 6, c is 12, divided by 2a, or 2 times 6. So we have negative times negative 17, that becomes positive 17. Negative 17 squared is going to be positive 289. And then we have negative 4 times 6, which is negative 24. times 12, that's going to be negative 288. 2 times 6 is 12. And inside the square root symbol, we have 289 minus 288, which is the square root of 1. And the square root of 1 is 1. So this is what we now have. So we have 17 plus 1 over 12. At this point, when you have the plus and minus symbol, you can break it up into two answers. And the other answer is going to be 17 minus 1 over 12. 17 plus 1 is 18. And 17 minus 1 is 16. So now, we just need to reduce those fractions.
So 18 is 6 times 3, 12 is 6 times 2. Canceling the 6, we get one of our solutions as 3 over 2. For the other one... 16, we can write that as 4 times 4. 12 is 4 times 3. So canceling the 4, we get the other answer, which is 4 over 3. And so that's it for this video. Now you know how to use the quadratic formula to solve a quadratic equation.
Thanks again for watching.