Completing the square is a way to simplify polynomial expressions
by writing them as sums or differences of squares. The method
goes like this:

- Starting with an expression such as this:
*Ax*^{2} + Bx + C

- Divide through by A so that the
*x*^{2} term has a
coefficent of 1.
*x*^{2} + (B / A)x + (C / A)

- Add and subtract one half (B / A) squared.
*x*^{2} + (B / A)x + (B / (2A))^{2} + (C / A) -
(B / (2A))^{2}

- The first three terms of the above expression can be written as
*(x + (B / (2A)))*^{2}

This can be verified by multiplying the expression out.
- The finished formula can be written as
*(x + (B / (2A)))*^{2} + (C / A) -
(B / (2A))^{2}

- Multiplying out the last two terms gives us a total result of:
*(x + (B / (2A)))*^{2} + (4AC -
B^{2}) / (4A^{2})