How to Calculate the Quadratic Formula

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The quadratic formula is one of the most fundamental formulas in mathematics, and it is expressed as X equals negative B plus or minus the square root of B squared minus four AC over two A. Calculate the quadratic formula with instructions from a college-level math teacher in this free video on geometry.

Part of the Video Series: Geometry Tips
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How do you calculate the quadratic formula? Hi, I'm Jimmy Chang. I've been teaching college mathematics for nine years now and the quadratic formula is one of the most fundamental formulas that you will ever learn, so I highly recommend that you go over it as much as possible. So here's a brief lesson on how it came about. First of all you may have seen that a quadratic equation is of the form ax squared plus bx plus c. If you notice, every term is on one side and zero is on the other side and notice a is the number right next to the x squared. B is the number right next the x and c is simply the number with no x term. So c is known as the constant. But everything is over to one side and zero is on the other side. And to solve it, to get x by itself. This quadratic formula came about. It's negative b, plus or minus square root of b square minus 4ac, all that over 2a. Now, here's an example as to how you solve this particular equation using this formula. Now, suppose you have x squared plus 2x minus 3 is equal to zero. As long as you identify your as bs and cs, you'll be good to go. Now, because there's no number in front of the x squared, you can always assume that a is equal to 1. B, the number next to the x is positive 2, and c is negative 3. What you need to do is plug in everywhere you see a, you plug in 1. Everywhere you see b, plug in 2. Everywhere you see c, negative 3. So this is what the formula looks like. X is equal to negative b, so you have negative 2, plus or minus, square root of 2 squared, minus 4, times... a is 1. C is negative 3. All that over 2 times, a is 1. The hardest part about this problem is simplifying everything inside the radical. So, you have negative 2 plus or minus square root of, 2 squared is 4. Negative 4 times one is negative 4. Negative 4 times negative 3 is positive twelve... over 2. Now, 4 plus twelve is going to give you 16, so you have negative 12, plus or minus square root of sixteen, all that over 2. Now, square root of 16 is indeed 4, so up here, you now have negative 2, plus or minus 4, over 2. Now this is 2 answers. You need to break them up as two separate solutions, but once you have them, you've solved the equation. I'm Jimmy Chang, and that's how you calculate the quadratic formula.

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