Hi it's Carlea McAvoy talking about solving
quadratic equations using the quadratic
formula
these are the four problems i'm going to
solve in this video but first i want to
look at the quadratic equation ax
squared plus bx plus c... a is the
coefficient of the second degree term b
of the first degree term and c is the
constant and when you look at the
formula over here x equals negative b
that's the opposite of whatever your b
is here plus or minus that's how we get
two different solutions the square root
of b squared minus 4ac a being the
coefficient of the second degree term
and c being the constant term all over
2a
so that's the formula we're going to
plug into whenever we want to solve
quadratic equation we want to make sure
that our equation is equal to 0 so for
this first one the first thing I'm going
to do is move that 1 over to make
it negative 1 so that i can then solve
the equation using the quadratic formula
so i'm going to write down (I think this is a
good idea for everybody) write down what
you're a, b, and c is. a is 2... B is
-9 and c is negative 1 so i have x
equals negative negative 9 which is 9
plus or minus the square root of b
squared which is 81
minus 4 times a times c all over 2 times
a well
a is 2 so two times two is four and
what I want you to see here is I have a
negative and another negative and since
i have two negatives that's gonna make a positive
so I have nine plus or minus the square
root of 81 plus 8 which is 89 and that's
over 4. Now if you're not sure
89 can be simplified or not because
remember when you get another video
where we said you can't leave a radical
like that if it's not simplified you can
just go into your calculator if you have
a calculator that will do this for you
just put in the 89 and hit enter it does not
simplify it still the square root of 89
what if i did one that would be
simplified like 75 then it will show you
that's 5 square root of three
ok what if i had i wanted to decimal i
would put in a point right now we get
the decimal answer for that but we don't
usually want decimal answers and we're
solving these we want the exact answer
which is the radical form so then i
could say this is my final answer
there's two answers in there or I could
say this is 9 plus the square root of 89
over 4 & 9 minus the square root of 89 over
4 there's two answers in there
whichever way you write it if you're on
paper this is a nice way to do it
sometimes on the computer you have to
separate them out
this one's ready to go a is 3 b is negative
20 and c is negative 7
we have x equals negative B so the
opposite of b is 20 plus or minus the
square root of b squared which is 400
minus 4 times 3 times negative 7 so make
sure you're using the signs including
those signs in there correctly all over
2a 2 times 3 is 6
now you can simplify inside the radical
separately all at once whatever you want
to do I got plus or minus over 6 so I'm
going to simplify my I'm not
going to put a decimal in because i
don't want a decimal answer i just want
to see what that would simplify out to
be so second function radical 400-4 times 3 times -7
and make sure when you put the negative
and use the negative sign not the
subtraction sign negative seven so
that's what i have in there and I'm
going to hit enter
and that's just 22 thats the perfectly worked
out nicely so I have 22 and so then I
have two different solutions that I want
to look at 20 plus 22 / 6 and 20-22 over
six well 20 plus 22 is 42 over 6 which
is 21 which is seven right
yeah took me a minute there and then
20-22 is negative 2 / 6 and that's
negative 1/3 so we have two
solutions which is what we expect unless
we have a perfect square trinomial and
that's going to be our two answers okay
number three again we need to move those
things to make that half and equal to 0
so when they move negative 2x I get
positive 2x and when i move positive 2
i get negative 2 because i'm doing the
opposite across the equal sign these all
have a common factors too if I wanted to
I could just divide everything by 2 and
get x squared plus X minus 1 equals 0
and that just gives me smaller numbers
to work with but if I didn't want to do
that I could have used the numbers as
given a is 1, b is 1, and c is a
-1 so i have x equals negative
b thats negative 1 plus or minus the
square root of b squared while 1 squared
is still 1 minus 4 times a times c
all over 2 times 1 which is just 2 and
so i have negative 1 plus or minus and
this is negative 4 times negative 1 is
positive 4 plus 1 square root of 5
all over 2. I know square root of 5
can't be simplified i'm not even going
to write that out into separate pieces
i'm just gonna stop there
what if I had done the other numbers
would i get the same answer while let's
see if I said a 2, b is 2, and c is
negative 2
I would have gotten negative 2 plus or
minus the square root of b squared which
is 4 minus 4 times 2 times negative 2
all over 2 times 2 which is 4 while
inside here i have negative 4 times
negative 2 is positive 8 times 2 is 16
so i get the square root of 20 all over
4 and 20 looks like this
square root of 4 times the square root of 5
right? So 20 is actually negative 2 plus
or minus 2 square root of 5 over 4 and
then I say well i have a common factor
of 2 goes in here once goes in here
once goes in here twice and look what i get i
get the same answer I just had to reduce
at the end so reducing at the beginning
just saved me time  so you can always
divide out if it makes things easier for
you in the beginning here it would make
things easier because we don't have a
common factor we would just get crappy
fractions we don't want that so a is
three b is negative 20 and c... whoops I
copy down number two again! ah heavens.
let's try this actually we have negative
10x the problem should be 3x squared
minus 10x equals 25 and so i have 3x
squared minus 10x minus 25 this should
be 10x are just 10 sorry and c should be
negative 25 i had to move that over to
make that happen
now i have x equals negative B is going
to be positive
plus or minus the square root of b
squared which is 100 minus 4 times a
times C all over 2 times a which is six
ok
I could go through the motions of
simplifying that or I can let my calculator
do that for me
I have skills but you know sometimes I don't
want to do. so 100 minus 4.... times
3 whoops i need to go times 3 times 3 times negative 25 is
20
that's exactly 20 nice it's always nice
and things work out nicely you can see
four times five is a hundred is positive
100 times 3 is 300 + 100 is 400 square
root of 400 is 20... the computer did that for us
we have 10 plus or minus 20 / 6
so we have 30 / 6 or minus is negative
10 / 6 and that gives us five or
negative 5/3 and not using the
quadratic formula to solve equations
have a great day
