SOLUTION: factorise 100n^2 + 400n - 32,000 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: factorise 100n^2 + 400n - 32,000 = 0      Log On


   

Question 732876: factorise 100n^2 + 400n - 32,000 = 0
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
100nē + 400n - 32,000 = 0

Factorise 100

100(nē + 4n - 320) = 0

Write down all the ways to factorise 320, starting
with 320·1 and since the last sign is - write the 
difference of the two factors to the side:

320·1    320-1 = 319
160·2    160-2 = 158
 80·4     80-4 =  76
 64·5     64-5 =  59
 40·8     40-8 =  32
 32·10   32-10 =  22
 20·16   20-16 =   4

We find the coefficient of the middle term, which is 4,
in the list of differences, so we use 20 and 16:

100(n + 20)(n - 16) = 0

To solve that we use the zero-factor principle:

100 = 0; n + 20 =   0;   n - 16 =  0 
              n = -20;        n = 16

Edwin