Associated Topics || Dr. Math Home || Search Dr. Math

### Solve by Factoring

```
Date: 13 Mar 1995 11:29:24 -0500
From: Richard Seguin

Hello I had a question in math class like this today:

3w^2 + 40w - 25 = 20 - 2w^2

We are doing a section On Solving Equations by Factoring.
Could you help me?
```

```
Date: 13 Mar 1995 21:53:19 -0500
From: Dr. Sydney

Hello again, Richard!

Okay, for your problem, our final goal is to find what values of w make the
equation hold true.  The way we usually do this is to get everything on one
side of the equation, so we have an expression with w's and numbers on the
left, and 0 on the right.  Here is what I mean:

Subtract 20 and add 2w^2 to both sides of the equation.  Then you get:

3w^2 + 40w - 25 - 20 + 2w^2 = 0

Combine the w^2 terms with one another, and do the same with the constant
terms to get:

5w^2 + 40w - 45 = 0

Now, do you see anything that factors out of the left hand side?  All of
the terms on the left are divisible by 5, so let's divide each side of the
equation by 5.  We then get:

w^2 + 8w - 9 = 0

This is much simpler to work with, yes?

Okay, now we simply need to factor this quadratic.  I always do this by
playing around with the numbers...  We know that if this factors nicely, it
will factor into two terms that look like this:  (w + a)(w + c), where a and
c are constants.  Now, since the constant term is -9 we want ac to be -9.
And, since the term with the w has a coefficient of 8, we know that we want
a + c = 8.  (this is because (w+a)(w+c) = w^2 + (a+c)w + ac).  You can
figure out what a and c are by using these two equations, or you can simply
try a few numbers and see if you can find something that will work.

See if you can figure out what a and c are... Can you factor this one?
Write back if you want to check your answer, or if you have any more
questions!

--Sydney, "Dr. Maaaaath"
```
Associated Topics:
Middle School Factoring Expressions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search