Expert: Richard J. Raridon - 10/30/2011

Question
QUESTION: Is it possible to find an exact answer to this problem:
-3.0241 = b x b + b (or b squared +b)

Its not for homework...
my own experimenting...
This part isn't the sole purpose to my experimenting, just a block in the road. I've not yet taken trig, and I can't remember what my algebra teacher said about problems like this last year.
If you can get an exact answer, how do you do it? I remember something last year where you'd end up with two answers, but the memories are kind of vague and I'm not sure if that has anything to do with this problem. Even if there is a really complex way of finding it, I'd like to know.
Thanks -Angie

ANSWER: Never use an "x" to indicate multiplication.  Rewrite it b^2+b+3.0241 = 0
which is a quadratic equation.  b = [-1 +/-(1-12.0964)^1/2]/2  = [-1 +/-3.331i]/2
imaginary solutions

---------- FOLLOW-UP ----------

QUESTION: Wow. That's a lot more complex than I had expected... but where does the "12.0964" come from? And where did the "i" come from? One more question, what are imaginary solutions? I've never heard of them.
Thanks -Angie

Answer
You should have learned how to solve quadratic equations in algebra.  
If you have the equation ax^2+bx+c = 0, x = {-b +/-(b^2-4ac)^1/2]/(2a)
so in your equation, a=1, b=1 and c=3.0241 and 4ac = 12.0964
The equation doesn't have any real solutions since b^2-4ac = -11.0964 and you can't
take a square root of a negative number.  i = (-1)^1/2