Expert: Richard J. Raridon - 8/26/2008

Question
We were given a sample equation and was told that the method to solving quadratic equations came from India and to follow the steps, but I'm not sure where the 12x went. Could you please explain?

           x^ + 3x - 10 = 0
step 1        x^ + 3x = 10
step 2       4x^ + 12x = 40
step 3       4x^ + 12x + 9 = 40 + 9
            4x^ + 12x + 49
step 4        2x + 3 = +_7
step 5 2x + 3 = 7       2x + 3 = - 7
      2x = 4           2x = - 10
       x = 2            x = - 5

So where did the 12x go during the process of taking the square root of both sides in step 4?

Thanks in advance for your help!!  

Answer
First of all, it should be x^2+3x-10=0
Step 1 - x^2+3x = 10
Step 2 - 4x^2 +12x = 40
Step 3 - 4x^2 +12x +9 = 40 +9 or (2x+3)^2 = 49
  4x^ +12x +49 is wrong
Step 4 - take the square root of each side to get 2x+3 = +/- 7
Step 5 - 2x+3 = 7 so x = 2 or 2x+3 = -7 so x = -5