How To Solve Quadratic Equations

Hi, my name's Charles and I'm one of the math teachers from the Maxim Workshop. I'm just going to now teach you how to do some math. I'm going to show you how to solve quadratic equations.

Now, the first thing you need to know about quadratic equations is the general formula. Whenever you're trying to identify whether you've got a quadratic equation, you have to check if you have this a x squared plus b x plus c. Now, a is the coefficient of x squared, b is the coefficient of x, and c is your constant.

Now with these two, a and b, coefficient is just a jazzy name for a number that multiplies by it. Okay, so a multiplied by x squared and b multiplied by x. Now, we're going to insert some numbers just to give you a feel of what a quadratic equation looks like, and most of you already know.

So we've got 1 for a, just to keep it simple at first, plus 2x, plus 1. Okay, so this is the equation that we're going to start off with. Now of course, we need to be able to solve our equation and that means we need an equal sign if it's going to be an equation.

Now what we're trying to do is see where these values of x makes this whole equation go to zero. Now in order to do this, we're going to use factorization. Factorization is just basically putting our quadratic equation into two brackets so that makes it easier to see where the solutions are.

Now, first thing we're going to do is get our two brackets, and for this we notice that we've got x squared, so we've got our two x's here. So this multiplies by this, now this will also multiply by this and our term here will multiply by the two terms inside this bracket. Now, the first thing we want to do is see what are the factors of this particular number, i.

e. the constant. So the factors of 1 are basically just 1 and 1.

So those are the only two numbers that we can use. As well with this number, we need to identify the factors of this number as a summation to acquire this number. So if you look at these two factors here, 1 and 1, when added together produces two, so the only solution is one and one.

So we've got one positive here and one positive there. Now in order to make this bracket go to zero, x has to be a particular number and in order to make this bracket go to zero, x also has to be a particular number. Now, we can see for this bracket x is going to be negative one, similarly if we take a look at this, it just so happens that x is also negative one.

So the two solutions that we have are the same number. So, x equals negative one is the value that takes this equation to zero.