The product of some negative number and 4 less than twice that number is 240. Find the number.

Question

I need help setting up this equation.

Answer 1

Let         n = the negative number

Let 2n - 4  = 4 less than twice the number

 

Our equation is

 

     n(2n - 4) = 240

     2n² - 4n = 240

 

Simplify by dividing by 2

 

     n² - 2n = 120

     n² - 2n - 120 = 0

 

Factor

 

    (n + 10)(n - 12) = 0

   

Solve using zero product property

 

   n + 10 = 0

   n  = -10

 

Or n - 12 = 0 ... n = 12 ... discard. because the number is supposed to be negative

 

The number is -10

 

Answer 2

Let x=the negative number

 

The other number is 4 less than twice x

 

Or 2x - 4

 

Now take the product of x and (2x-4).  That must equal 240

 

Hopefully this helps you get the equation and then solve for x

 

Hope this helps

 

Tom