Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to show you how to solve a quadratic equation using the complete the square method.Let's take a look at this word problem. Suppose you throw a ball straight up into the air at 40 meters per second. How long will it take for the ball to reach 35 meters if the height is given by the following function: 40t – 5t²? So we set the height equation to negative 35 meters. The first step is to change this lead coefficient from negative five to one, and we do this by dividing out negative five into every term. That gives us a negative seven, equals negative eight t, plus t squared.The next step in the complete the square method is to rewrite the right side of the equation into a perfect square form. I'll leave this term inside here blank for now, and then we might get something over here. So the first thing you want to do is divide out this negative eight by two to give you negative four, and you write that negative four right inside the square. Then you're going to go ahead and square negative four to give you 16, and you have to subtract it on this side. Now your expression is exactly the same, or equivalent to the one above.And to find the solution, you want to get everything that's not part of the perfect square to one side of the equation; that means you want to add this 16 to both sides of the equation. That gives you nine equals t minus four squared. And you can take the square root of both sides (and when you take the square root you have to do plus or minus) so the square root of nine is plus or minus three equals t minus four. And now you can just solve for t – you're going to get two answers because of this plus or minus. So it's t equals, if we say plus, seven; or t equals one, if we assume that it's minus three. And now we have our two solutions because the ball goes up and down past 35 meters twice.Thanks for watching, and to learn more, visit us on the web at About.com.

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