This video is going to be about solving quadratic equations with the square root method,
and this is really a pretty easy thing to
do. So here's an example.
I've got x squared minus 25 equals 0,
and I want to find out what x is.
So the first thing I'm going to do is
isolate the x squared,
which means, in this case, 
I'll add 25  to both sides.
That's going to give me
x squared
equals 25.
Now if you stop for a second 
and see what I've got here,
you realize what this 
equation is saying is
there's some number 
that we're calling x,
and when I square that number
I'll get a 25.
Now you know you can multiply 5 times
5 and get a 25, but don't forget
you can also multiplied two negative
numbers
and get a positive.
So
we could have had
x equaling 5
or x might have equaled negative 5. 
Negative 5 squared is also 25.
So what I'm going to do
is I'm gonna write x, I'm gonna 
think of myself as taking the square
root of x squared,
and then I'm going to have
the positive and negative
square roots
of the right side 
of the equation, of 25.
In other words, 
x could equal
the positive square root of 25
or it could equal the negative 
square root of 25.
Now the square root of 25 is 5,
so I'm going to have x equals plus
or minus 5.
And if you plug
both plus and minus 5 back into the
original, you'll find they balance
either way.
So 5 squared is 25, minus 25 is 0. 
Negative 5 squared
is 25,
minus 25 is 0.
So what you're doing, 
the basic method is
isolate the variable,
the x squared, in this case.
So you have the x squared on one side, 
you have the constant number the other.
Then,
take the square root of the x squared, 
which will be x,
and the positive and negative 
square roots of the constant.
And then find out what that 
square root is.
Here's a few more examples.
In this one, 
I've got x squared
minus 8 equals 0.
So
isolating the x squared,
by adding 8 to both sides,
we get x squared 
equals 8.
So
x
is going to equal
the positive and negative
square roots
of 8.
Now we're not done, because we have to
simplify this radical.
I know that 8 is 4 times  2, 
and 4 is a perfect square.
So I'll have x equals
plus or minus
the square root of 4 times 2,
and now I'll just pull out 
the square root of 4.
So x equals
plus or minus
2
times the square root of 2.
Here's another one.
x squared minus 7 equals 11. 
I want to isolate my variable,
so I'll add 7 to both sides.
On the left side 
I just get x squared.
On the right side I've got 
11 plus 7 is 18.
So
x is going to equal
the positive and negative 
square roots of 18.
And now I've just got to simplify 
the square root of 18.
So x equals plus or minus 
the square root of...
18 is 9 times 2,
9 is a perfect square.
So I'll take that square root out.
x equals plus or minus
3
times the square root of 2.
So reviewing this once again,
you want to isolate
the variable
on one side of your equation.
You'll probably have to 
add or subtract something,
and we'll get 
the variable on one side
and a constant on the other.
And then you're going to
take that variable, which was squared, 
and take its square root as an x
or whatever it is, and on the right side you're going to have plus or minus the square root
of whatever the constant was, and then
just simplify that square root.
So that's all there is to this. 
There is one place I want to warn you about.
So look at one more example.
Here I've got x squared plus 16 equals 0.
So if I want to isolate the x squared,
I'll subtract 16 from both sides.
And now I've got x squared
equals
negative
16. Okay, let's stop and look at this.
This is saying that 
I've got some number,
which we're calling x,
we're squaring it and 
ending up with a negative 16.
Well, this impossible
because
if I square 4... 4 times 4 is 
positive 16.
If I square
negative 4,
negative 4 times negative 4 is also
positive 16. So if you see a
situation like this where 
you have a square on one side
and a negative number
and the other side of the equation,
don't go any further. 
Just write "no solution"
and go on to the next problem.
So that's really all there is to it.
I'll see you next time.
