Expert: Josh - 3/23/2004

Question
I have a problem that looks like this:
1/2[a+b(squared)]c = 3(a-c)
Can you tell me how to solve this for the specific variable "a", in a step-by-step manner Pah-leeeeze!  I have the answer already, but I need to know how to work the problem.  Thank you!

Answer
Hi Crystal,

I am not clear about your question.
Does it read 0.5*[a+b^2]*c=3(a-c)?
If so,
0.5*a+0.5*b^2*c=3a-3c
0.5*b^2*c+3c=(3-0.5)a
a=(0.5*b^2*c+3c)/2.5

On the other hand, if we have
1/[2c(a+b^2)]=3(a-c) ...cross multiply
1=3(a-c)(2c(a+b^2))  ...expand
1=3a(2c(a+b^2))-3c(2c(a+b^2))
=6*c*a^2 + 6*c*b^2*a -6*c^2*a -3*c^2*b^2

You obtain a quadratic in "a"
6*c*a^2 +(6*c*b^2-6*c^2)*a -3*c^2*b^2-1 = 0
Letting A=6*c, B=6c(b^2-c), C=-3*c^2*b^2-1
You can find out "a" using the standard quadratic formula.
Namely, a=[-B+sqrt(B^2-4AC)]/(2A),[-B-sqrt(B^2-4AC)]/(2A)

You can check the details.

You see, the problem is entirely different.
Pls. use parenthesis and superscript (like a^2) in future to avoid ambiguity.

Cheers.