Hello I'm Bob Rose and I'd like to
welcome you to the 20th Joy of Painting...
Let's do some real art.
Quadratic Formula.
So what is the quadratic formula?
So you can sing it. Or you can just
memorize it. And this is how it's written.
And so the thing we need to know here is
that we have these a's, b's, and c's and a
b and c come from the standard form of
the quadratic equation. Alright so we
have a, b, and c. Now in this question that
we're working here, we have
8x^2 + 8x = 22. Be careful on a
question like this. C is not 22. We need
to get this 22 over to the left hand
side and have 0 on the other side before
we can begin the quadratic formula for this question. Alright so we get
8x^2 + 8x - 22 = 0. And now we
recognize here that: this is a, this is b,
and that number right there... -22...
is c. And now we can play and chug...
So we have negative... and then our b was 8... plus or minus the square root of b squared
minus 4 times a times c. I'm
going to divide that by 2 times 8.
Alright so you see so far, it's just been a
simple substitution of a, b, and c... 8, 8, and
-22. Ok, so we're going to take
this and continue to work with it. So
-8 plus or minus the square root
of 8 squared is 64 and then -4
times 8 times 22 is 704. And there's two
negatives here so we'll say plus 704
divided by 16. And we continue on here...
and 64 + 704 will be 768...
over 16. At this point, I have put this
answer into WebAssign and it will mark
this correct. But typically we will come
back and simplify something like the
square root of 768. But for the purposes
of this question, this step is totally
optional. I'll just shortcut right
straight to the answer. I have found out
that 768 is the same as 256 times 3. And
the square root of 256 is 16 square root
of 3. So if you're going to continue
working with this... again you can stop at
this point if you like and enter that...
but we would write 16 square root of 3
over 16. And now we can cancel anything
here that is outside of this radical if it
is divisible by same number. So 8 goes into 8 once...
8 goes into 16 two times and 8 goes into 16 two times. So you may also enter for this
answer, -1 plus or minus 2 square
root of 3 over 2 and WebAssign will also
accept that answer.
