Expert: Richard J. Raridon - 6/23/2009

Question
I have a question regarding an example given in a text book. It involves the method for solving quadratic equation from India.  I found that someone had previously asked you this question on this example.  There question was where did 12x go to, and I have an expanded question on the subject.  
Here is the problem:
X2 + 3x – 10 = 0
Solved until this point such as:
X2 + 3x = 10
4x(exp2)+ 12x = 40
4x(exp2)+ 12x + 9 = 49
2x + 3 = 7
My question is this: 12 does not square evenly, where does the 3 come from?
Thank you in advance!

Answer
Well, first of all this one is easy enough to factor to get
(x+5) and (x-2) so x = 2,-5.  
What you're doing is completing the square so that
4x^2+12x+9 = (2x+3)^2   
Now, however, you need to write
(2x+3)^2 = 49 so 2x+3 = +/-7
If 2x+3 = 7, then x = 2; if 2x+3 = -7, then x = -5
4 and 9 are perfect squares, 12 doesn't have to be.