-2x^2-28x-96=0 and 6m^2+12m-144

Question

Please show work 

Answer 1

I assume you need to solve for x and m respectively.

 

1)  -2x² - 28x - 96 = 0

      We can factor a -2 from each term so let's do that first

     (-2x² - 28x - 96)/-2 = 0/-2

      x² + 14x + 48 = 0

     Since the last term is positive we try to factor.  Look for factors of 48 that add to 14.  That is 8(6)

     because 8(6) = 48 and 8 + 6 = 14 so this factors to

     (x+8)(x+6) = 0

     For this to be true either

     x+8 = 0      or     x+6 = 0

     x = -8 or x=-6

 

You can plug that into the original equation to check answer... 

 

2)   6m² + 12m - 144 = 0

      We can divide 6 out of every term so again let's do that

     (6m² + 12m - 144)/6 = 0/6

      m² + 2m - 24 = 0

     Since the last term (the constant) is negative look for factors of -24 that add to 2.  One factor will be

     positive and the other negative.  Look also at the 2nd term (2m) which is positive.  That means the

     larger factor of -24 we use will get the positive sign.

     Factors of -24 that add to 2 are (6)(-4)

     m² + 2m -24 = (m+6)(m-4)

     Setting this equal to 0 we have

     (m+6)(m-4) = 0

     As before this only works if m+6 = 0   or   m-4 = 0

    So m = -6 or m = 4