Quadratic Formula Example 2.
f(x)= -2x² + 10x - 4.
So, our a value here is -2,
our b value
is 10,
and our c value would be a -4.
Plugging that into
our quadratic formula we would have x equals
-10
plus or minus the
square root of 10²
minus 4
times -2 times -4.
All divided by
2 times -2.
Simplifying inside of our square root.
We would have
10²
minus
4 times -2 times -4.
I can just plug that into my calculator
that will give us 68,
inside
or under our radical.
2 times -2,
-4.
So, ow we need to simplify a radical.
To do that I need to find some factors that will go into 68.
68 is divisible by 4.
Let me do that up her in a different color.
So 68 would be 4 times 17.
So, 4 is a perfect square,
17 is a prime number so we can't do anything with that.
So we could rewrite that
as √4 times √17.
Simplifying then,
I would have
x equals -10 plus or minus
2,
times the square root of 17. Take the square root of 4 that gives us 2,
17 stays inside.
All over -4.
So, to get our exact answer now ...
we need to simplify, if I look at all of these
I should see 10,
2, and 4 all of those are even ...
numbers that means I can divide all of those
by 2.
And I'm actually going to divide all those by a -2.
To get rid of the negative in my denominator.
So,
10 or
-10 divided by -2 will give me 5,
plus or minus
2 divided by -2 would be a -1.
But since we have a plus or minus that kind of cancels it ...
out, because we do have both.
So √17.
Over and the -4 divided by -2
would be 2.
So that would be our simplified.
We can write it just like that for our exact answer we don't ...
need to split it up.
If your teacher wants you to split up,
then you would have  5 +√17
over 2.
And x = 5 - √17
over 2.
Okay.
Then we're going to find our
decimal answer.
To do that I'm going to put this into my calculator.
I'm going to put it in, in parts,
I'm going to do the additional person that would be 5 plus
our square root of 17, and I'm going to go ahead and hit enter.
If your calculator gives it to you in radical mode still,
you need to just go into mode.
and change that. You'll have to go all the way ...
down to the bottom, use your arrow keys,
and we want to be in classic instead of math print and hit enter.
And then if you quit out of mode.
Starting again 5 plus
square root
17.
Give me a decimal and that needs to be divided by
2.
So, that's my first decimal answer.
To three decimal places I believe is what we were ...
rounding to earlier, that would be 5,6 and that ...
five there will round up to a 2.
So x would equal
4.652.
Then our next one, x will equal...
o then we need to do the minus version
So 5
minus
square root of 17.
Enter.
Divided by 2.
So that will be 0.43844, so that four is not going to ...
round our 8 up.
So, 0.438.
Those would be our
exact
and our decimal
answers.
Now if I didn't split it up like this on my calculator as the ...
two separate entries.
Then you would need to make sure you use parentheses
when you insert or type in the first part.
So you would need parentheses 5 plus
do you square root...
Now notice your square root puts a parentheses in also.
So, when you end it you need to ...
put two parentheses:
to end both the radical and then to end the numerator of ...
the fraction. And then you would divide by 2.
And that would give you the same answer we got that first ...
time. If you try it without ...
parentheses if I just did 5 plus
√17 divide by 2,
I'm going to get a completely different answer.
That's because your calculators are following ...
order of operations and its dividing before it adds to ...
those parentheses are very important,
which is why I recommend you do it in two steps instead ...
of trying to do it in one step.
So again our answers.
Our exact.
x would equal
(5 + √17) all over 2, or
x would equal (5 - √17) all over 2.
Four our two decimal answers 4.652
or
0.438
