Suppose we have the expression:
If we expand it, we get:
Now suppose if b were to be divided by 2 from the beginning, then:
Lets say we subtracted this expression by (b/2)2:
Now we are confident enough to say that:
Now lets look at the quadratic equation:
Lets bring c to the other side and divide both sides by a:
If we simplify:
We learnt how to expand [x2 + bx], now lets expand [x2 + (b/a)x]:
Lets rearrange the equation:
Lets multiply c and a by 4a:
Now lets square root both sides:
The ± only needs to be at either the numerator or the denominator. If we make x the subject:
We finally get our formula:
