(Posted this on mymathforum.com as well. This is a copy-paste)
I'm a Swedish student, reading course C in mathematics. I've read course A and B before, but it was more than five years ago, and I've forgot about everything (they predict that everyone knows course A and B).
I'm having problem with factorization and equations.
I can solve very easy equations like x^2-4x+3 and stuff like that. What I'm having trouble with are √-equations.
I can solve for example √(2x+5)=x+1 by doing this:
1. 2x+5 = (x+1)^2
2. 2x+5 = x^2+2x+1
3. x^2-4 = 0
But then, when I come to this problem, √(4t+1)=3-3t, I can't solve it:
1. 4t+1 = (3-3t)^2
2. 4t+1 = 9-18t+9t^2
3. 9t^2-22t+8 = 0
4. What here? The answer is (4/9). I know that I somehow should divide everything with 9. Should I first calculate everything and the divide by 9?
Two more problems: 3√(x+13) = x+9 & √(x+1)-1=x. How do I solve this?
In short: How do I get the answer 7(x-1)(x+2/7) from 7x^2-5x-2? Are there any steps/formulas to get to this answer? How do I know that 7x^2-5x-2 should be written in the form a(b-c)(b+d), and not something like a(a-b-c) etc. When I know that it should be written like a(b-c)(b+d), how do I calculate what should be in "c" and in "d"?
I hope I've explained my problems well. As said, I haven't done any mathematics in over five years, and the course expect me to know course A and B already, and I feel totally lost.