Hi, my name is Gloria Blagg and today we will 
talk about quadratic formula.
Ok, Today we are discussing the quadratic 
formula
which is x equals negative b plus or minus
the square root of b squared minus
4 times a times c all over
2a. This method is used for solving
quadratic formulas in the form ax squared plus 
bx
plus c equals 0. Where you plug in
a, b, and c into the formula as long
as the equation is already set to 0. Remember 
you
must set your equation
equal to zero.
 (Teacher Writing)
To define your a, b, and c.
 (Teacher Writing)
Ok, our first example, we are going to make 
sure our equation is in the quadratic form where 
it's
set equal to 0 so we can define our a, b, and c. 
a is always
the coefficient in front of x squared so a equals 5. 
b is the coefficient, including the sign, in front of 
x, so b equals
negative 14. And c is the constant so c equals
negative 3. Be sure you include the signs in front 
of each number.
Now we are going to put in our a, b, and c into 
our formula.
So looking at our formula we are going to just 
solve for x which equals negative
-I'm going to use parenthesis for each number- 
negative b.
I'll have a negative 14, be sure you put that 
negative in there.
Plus or minus the square root. Again I am going 
to use parenthesis where I'm
substituting b squared so it will be negative 14 
squared
minus 4, that’s always a four, times a,
times c. In place of a I'm going to put 5, in place 
of c
I'll put negative 3. All over 2 times
a, which is 2 times 5. Once you
have all the numbers into the formula, you use 
order of operations
to break it down. So we are going to get rid of all 
our parenthesis and
our exponents. So, minus a negative, we know 
that becomes a positive.
14, plus or minus. Negative 14 squared
becomes a positive 196.
And then multiplying here, this is all 
multiplication.
I would say count your negatives. I see two 
negatives there which tells me I'm going to have 
a 
plus. And then I just multiply the numbers. 4 
times 5 is 20, times 3
is 60. All over 2 times 5
which is 10. Keep going, we're going to break 
down
your radical as far as you can. I have 14, plus or 
minus.
196 plus 60 is
256 over 10. We always see if we can
simplify our square root, and we can.
The square root of 256 is a perfect square of 16.
I have 14 plus or minus 16 over 10.
Don't stop here, when the radical is gone you 
can actually do the
addition and subtraction. So we have two 
solutions. We have 14
plus 16 over 10 which becomes 30
over 10. Which equals 3.
We also have 14 minus 
16 over ten. Which equals negative 2
over 10. Which would reduce the fraction down 
to negative 
one fifth. And those are our two solutions for x.
Second example, we are going to look at our equation and see that it's not
equal to zero. So we need to move the 7 to the other side.
So I'm going to subtract seven to this side.
Leave me with 8m squared,
minus 2m, minus 7.
equals 0. Now I can define my a, b, and c.
a equals 8, b
equals negative 2, and c equals negative
7. Plugging a, b, and c into my
formula. x would equal
negative, again I am going to use parenthesis, negative
b which is negative two. Plus or
minus b squared, that would be negative
2 squared minus
4 times a, which is 8,
times c, which is negative seven.
All over 2 times a, again which is
8. Continue doing the order of operations.
We have minus a negative 2, which would become positive 2.
Remove that parenthesis. Plus or minus
negative 2 squared would be a positive 4. Again, count
you negative signs. I have two negative signs, a negative 4 and
negative 7. That's going to, when we multiply that out, become positive
224. All over 2 times 8 which is 16.
You're next step from there, 2 plus or minus
the square root of 228 all
over 16. 228 is not a perfect
square but it will simplify. You can break it down to the
2 plus or minus 4 times
57 over 16.
4 comes out as a perfect square to come out to be 2 plus or minus
2. That’s the square root of four, leaving 57 on the
inside all over 16.We can't
add or subtract, but you can look at the numbers on the outside.
On the outside they all reduce by two, so reducing
each one by two would give me 1 plus or minus
1 times the square root of 57, you don’t have to show that 1,
over, 2 goes into 16 and reduces to 8, my
two solutions are 1 plus square root of 57 over 8, and 1
minus square root of 57 over 8.
Ok, example 3, our equation is already set equal
to 0 so we can define a again. a is 1,
if you don't see a number in front of the variable you know the coefficient
is one. b is positive 6, and c is
positive 13. Plugging into our formula, 
x equals, again we have, negative b which is 6.
Plus or minus the square root
of b, 6, squared minus
4 times a, is 1, and c, is
13, all over 2 times a,
which is 1. Simplifying we get negative 6
because there is only one negative there, plus or minus 
positive 6 squared is positive 3. There's only
one negative sign, negative 4 times 1 times 13
would be 52. All over 2 times 1
which is 2. Now we have negative 6
plus or minus, simplifying inside the radical, 
36 minus 52 is negative 16. Again,
all over 2. You always want to simplify your radicals.
This is a perfect square with a negative
side which is an imaginary number so we end up with 6 plus
or minus 4i over
2. Now, 
you cannot add a real or an imaginary number, but again you can reduce
all three of these numbers by 2, which would simplify this to be
negative 6 divided by 2 is negative 3 plus
minus 4 divided by 2 is 2
i. So my two solutions are negative three
plus or minus 2i.
Example 4, we have y squared minus 8 equals 4y. We need to make
the equation equal 0. Again I am going to subtract 4y
over two the left side. Be sure you write your equation descending
order though to find your a, b, and c. So we have y squared
minus 4y minus 8 and that then
equals 0. Defining our a, b, and c.
Again a equals 1, Again, when you don't see a number in front of
the coefficient. b equals take the sign,
negative 4. And c equals negative 8
Plugging it in for our formula,
we have y is going to equal negative, again, b
we're going to put in negative 4. Plus
or minus b squared, which would be negative
4 squared minus 4 times a
which is 1 and c which is negative
8. All over 2 times a.
Which is 1. Simplifying further,
again minus a negative to get rid of the parenthesis, that becomes a positive 4
plus or minus, simplify inside the radical getting rid of
exponents. Negative 4 squared is positive 16,
Multiplying negative 4 times negative 8 times 1 would be positive
32. And that is all over
2. 2 times 1 is 2. Going
up here just to finish the problem, we have 4
what’s inside the radical. 16 plus 32 which is
48, all over 2.
48 is not a perfect square but it can simplify
actually break down 48 to be
16 times 3. And if you take the
square root of 16 it will come out as a 4. So we have
4 plus or minus the square root of 16 is
4, leaving a 3 on the inside; 2 underneath.
You can still simplify each one
has a number outside that reduces by 2. Leaving you with 2
plus or minus 2, times the square root of 3 over
1. And you do not have to show the one so those
are your solutions.
