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What is the sum of the \(x\) values that satisfy the equation \(5=\frac{x^3-2x^2-8x}{x+2}\)?

 

I cross multiplied and got: 5x + 10 = x^3 - 2x^2 - 8x.

 

What should I do next???

Guest Jun 15, 2018
 #1
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+1

Solve for x:
5 x + 10 = x^3 - 2 x^2 - 8 x

Subtract x^3 - 2 x^2 - 8 x from both sides:
-x^3 + 2 x^2 + 13 x + 10 = 0

The left hand side factors into a product with four terms:
-(x - 5) (x + 1) (x + 2) = 0

Multiply both sides by -1:
(x - 5) (x + 1) (x + 2) = 0

Split into three equations:
x - 5 = 0 or x + 1 = 0 or x + 2 = 0

Add 5 to both sides:
x = 5 or x + 1 = 0 or x + 2 = 0

Subtract 1 from both sides:
x = 5 or x = -1 or x + 2 = 0
Subtract 2 from both sides:

x = 5    or     x = -1     or      x = -2

Guest Jun 15, 2018
 #2
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+1

-2 doens't work because that would make the denominater zero, but other than that, thanks for the help!

Guest Jun 15, 2018
 #3
avatar+26758 
+1

You could also do it this way:

 

5 = (x3 - 2x2 -8x)/(x + 2)

 

5 = x(x + 2)(x - 4)/(x+2)

 

5 = x(x - 4)

 

x2 - 4x - 5 = 0

 

(x + 1)(x - 5) = 0

 

x = -1 or x = 5

Alan  Jun 15, 2018

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