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Question 171271: This came from a Factoring Polynomials Sections..
I need help finding all the solutions to
-17w=8w^2+5w-40
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! 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.
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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
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Do the same with the other factor.
w + 4 = 0
w = -4
Final answer: w = 5/4 and w = -4
Did you follow?
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