We can factor the expression as
follows:
To figure this out, we used the quadratic formula (see http://en.wikipedia.org/wiki/Quadratic_equation):
=
We recognized that y= is
a quadratic equation in the form of y=
where a=2, b=-5 and c=-10.
To confirm that our calculation are right, we decided to plot
the graph of y = by
plugging in various values of w.
As you can see, there is a root at approximately -1.3 and
another root at approximately +3.8. So we know approximately what the values of
a and b are. We could use a calculator to get closer and closer to the exact
values of a and b. For example, if we try w=3.8, we get a value of y = -0.12.
If we try a slightly different value, we can see if we’re getting closer to
zero or farther away: w=3.81 produces a value of y=-0.018, so we know that 3.81
is a better approximation than 3.8. If we keep calculating closer
approximations of the root, we will arrive at the value of b that we calculated
using the quadratic formula: