[SOUND] Let's learrn about the quadratic formula.

[SOUND] For example, let's use the quadratric formula to solve this equation

for x. [SOUND] And here's the quadratic formula.

It states that the solutions of quadratic equations of this form are given by X

equal negative B plus or minus the square root of B squared minus 4 A C all divided

by 2 A. And by the way, this is a direct result

of completing the square. And our equation here is of that form

where a is equal to 3, b is equal to 1, and c is equal to negative 2.

So the quadratic formula tells us that the solutions are given by negative b or

negative 1, plus or minus the square root of b squared or 1 squared, minus 4 times

a, which is 3 times c, which is negative 2, all divided by 2 times a, or 2 times

3, which is equal to negative 1 plus or

minus the square root of 1. And then we have plus 24, because it's

minus 4 times 3, which is negative 12, times negative 2,

which is +24, all divided by 6.

And this equal to negative 1 plus or minus the square root of 25 divided by 6,

or negative 1 plus or minus 5 divided by 6, which means x is equal to negative 1

plus 5 divided by 6 or x is equal to negative 1 minus 5 divided by 6.

And what are these two numbers? This is x is equal to negative 1 plus 5 is 4, and

4/6 reduces to 2/3, or x is equal to negative 1 minus 5 is negative 6, and

negative 6 divided by 6 is negative 1. So these would be our answers.

Now if we weren't told to use the quadratic formula here, we wouldn't want

to. Because doesn't the left-hand side here

just factor? It factors into (3x-2)(x+1). And therefore we would get x=2/3 or x=-1,

which are the same answers. But perhaps you didn't see the

factorization. So it's always okay to use the quadratic

formula. You'll get to the same answer.

Let's see another one. [SOUND] Let's use the quadratic formula

to solve for y. [SOUND] Again, there's the quadratic

formula. So in this case we have that a=2, b=5 and

c=-1. So by this formula, we have x is equal to

negative p, which is negative 5 plus or minus the square root of b squared or 5

squared, minus 4 times a, which is 2, and then times c, which is negative 1,

all divided by 2 times a or 2(2). And this is equal to negative 5 plus or

minus the square root of 25, and then plus 8, all divided by 4, which equal to

negative 5, plus or minus the square root of 33 divided by 4.

Therefore our answers are x equal to negative 5 plus the square root fo 33,

all divided by 4. Or x is equal to negative 5 minus the

square root of 33, divided by 4. Now unlike the first example, factoring

here would not have helped us. However, we could have solved this by

completing the square, and we would have arrived at the same answers that the

quadratic formula just gave us. And this is how we use this formula.

Thank you, and we'll see you next time. [SOUND]