Expert: Abe Mantell - 8/1/2011

Question
Hi! My maths is not terrific and I'm having a bit of trouble understanding how an equation that has already been worked gets from one stage to the other. The first stage is:
(2x)^2/(1.000 - x)(2.000 - x) = 50.5
I don't quite get how they turn it into:
4x^2 = 50.5(x^2 - 3.000x + 2.000)
and then into:
46.5x^2 - 151.5x + 101.0 = 0
Sorry for the long question!
Thanks for your help,
Erin

Answer
Hello Erin,

The equation is best written:
(2x)^2/((1.000 - x)(2.000 - x)) = 50.5
now multiply both sides by (1.000 - x)(2.000 - x) to get
(2x)^2=50.5(1.000 - x)(2.000 - x), now expand the product (1.000 - x)(2.000 - x)
4x^2=50.5(2.000-2.000x-1.000x+x^2)
4x^2=50.5(2.000-3.000x+x^2), now distribute the 50.5
4x^2=101.0-151.5x+50.5x^2, now subtract 4x^2 from both sides
0=101.0-151.5x+46.5x^2

OK, do you see it now?  Let me know if you have any other questions.

Abe