Question 171271
I Will set up the quadratic equation and allow you to factor.
 
-17w = 8w^2 + 5w - 40

Adding 17w to both sides and setting up equation to equal zero, I get this:

8w^2 + 5w + 17w - 40 = 0

We now combine like terms and get:

8w^2 + 22w - 40 = 0

To reduce those big numbers on the left side of the equation, I'll divide each number by 2.

After doing so, I get this:

4w^2 + 11w - 20 = 0

Can you take it from here?

If not, write back.

==========================

I received your reply.

You asked:

Is the answer -4w?

Think about it for a minute.

Have you solved for w?

To solve for a letter means that the letter must equal an answer.

In other words, w should equal some value.

Here is your quadratic equation as I reduced it in my first reply:

4w^2 + 11w - 20 = 0

We multiply 4 times -20 and get -80.

Do you see the middle term 11w?

I am interested in the coefficient of w or 11.

What two numbers when multiplied together will yield -80 but when added will yield 11?

How about 16 times -5?

Yes, 16 times -5 = -80 but when added 16 PLUS -5 = 11.

Are you following?

We now have this equation:

4w^2 + 16w - 5w - 20 = 0

We create two groups.

Let 4w^2 + 16w be Group A.

Let - 5w - 20 be Group B.

Factor each group individually or one at a time.

4w^2 + 16w becomes 4w(w + 4).

-5w - 20 becomes -5(w + 4).

We now have this set of factors:

(4w - 5) (w + 4) (w + 4) = 0

Do you see the quantity (w + 4)?

We only need one of them.

We are left with two factors:

(4w - 5) (w + 4) = 0

Set each factor = 0 and solve for w.

4w - 5 = 0

4w = 5

w = 5/4

=======

Do the same with the other factor.

w + 4 = 0

w = -4

Final answer: w = 5/4 and w = -4

Did you follow?