 
Section 9.3 number 10.
Solve the following equation
by the quadratic formula.
5x squared minus 7x
minus 3 equals 0.
Well, the first thing to do is
compare this equation to the
standard form of the
quadratic formula.
ax squared plus bx
plus c equals 0.
Or a quadratic equation.
And then we want to identify
a, b, and c.
So a is equal to 5 in the
equation that we're given.
b is equal to negative 7,
so keep the sign in
front of the variable.
And c equals minus 3.
 
And we're going to use those
identified a, b, and c to plug
into the quadratic formula.
Quadratic formula tells us that
as long as we start with
an equation the same as ax
squared plus bx plus c equals
0, then x will equal the
opposite of b plus or minus
the square root of b squared
take away 4 times a times c,
everything over 2a.
 
So we're going to feed the
a, b, and c into there.
 
So let's go ahead and do it.
x equals minus b.
b is a negative 7.
Plus or minus square
root b squared.
7 squared is 49.
Minus 4, times a is 5,
c is negative 3.
Everything over 2 times
a, which is 2 times 5.
Right here we have a subtract
and a negative.
So we're going to have those two
negative signs canceling
each other out.
 
So we end up with x equals 7
plus or minus square root 49
plus 4 times 5 is 20 times
3 is 60, all over 10.
So we just keep going and
crunching away at it.
x equals 7 plus or minus
root 60 and 49 is 109.
Everything over 10 still.
And now the root 109, we
would try to get in
simplest radical form.
But this does not factor down
and there's nothing we can do
to make it in simplest
radical form.
Or actually, it is in simplest
radical form as it is.
There's nothing we can do it.
So we're going to leave
it like that.
And you can show the answer
either like this, or you might
notice in the MyMathLab software
that you have to
split up the two answers.
So to split them up, you want
to put one first, then a
comma, then the other one.
So let's take the positive
sign first.
X is 7 plus root 109
all over 10 comma.
For the second solution is 7
minus root 109 all over 10.
And make sure that everything
gets put over 10, not
just the root 109.
And you might have to try a few
times to get the template
right using MyMathLab
when you're
entering in your answers.
It can be a little bit tricky.
Make sure that you turn off the
root symbol before you go
to put in your denominator of
10, or before you put in your
comma, things like that.
Because you will get scored a
wrong answer if your root
symbol keeps going and
the software doesn't
recognize the answer.
But as always, I check your
answers on a test so that I'll
see if it was just
a small software
mistake that you made.
 
