In this example, we're going to look at
solving a word problem using the
quadratic formula.
The length of a rectangle is 3 inches greater than the width.  
The area is 30 inches squared. Find the length 
and the width. Anytime I can draw a picture
that's the first thing I like to do.
We're looking at a rectangle, so let's
draw a picture of a rectangle.
It says that the length
is 3 inches greater than the width.
This means we could write
the length as the width plus 3.
That would mean our width is going
to be w. We're also given
that our area is 30 inches squared, so
I'm going to use the formula
A equals length times the width. We're
going to plug in what we know and solve
for w. 
So, we have 30 equals the length
times the width.
Now let's distribute this w.
We have w squared plus 3w.
Now we're gonna solve this by
setting it equal to 0
and use the quadratic formula.  We'll subtract 30 from both sides.
So we have
0 equals w squared plus 3w minus 30.
Now we could
see if we could factor this. Two numbers
that multiply together to give me -30
but add up to give me
that middle number 3. If we were
to actually list at all factors that
give us
-30, we would find that we cannot find
anything that would work. For this
problem,
therefore, this is a good situation where
you would want to use the quadratic formula.
Here's the quadratic formula and our
equation.
Let's first define what A, B, and C are.
A is one since the coefficient of w squared
is one.
B is 3, 
C is -30. Now let's plug in our values
into our quadratic formula and simplify.
Three squared is 9.  Negative 4
times one times -30 is positive 120.  
Two times one is 2.
Nine plus 120 is 129.
At this point, I would check to see if I
could simplify
the square root of 129; however, the
square root of 129 cannot be simplified
any further. Therefore this is our final
answer.
