Completing the square is a technique used in algebra to create an expression which is a perfect square where none existed before. The presence of a perfect square form in an expression can often simplify the steps in an algebraic process. Perhaps the most notable use of completing the square is in the solution of quadratic equations and ultimately in the derivation of the famous quadratic formula. As an example, consider the quadratic equation x² + 6x - 17 = 0. The expression on the left side of the equation is not a perfect square, but since (x+3)² = x² + 6x + 9, adding 26 to both sides of our quadratic equation will give x² + 6x + 9 = 26, which is equivalent to (x+3)² = 26. Now the advantage of having the perfect square on the left side of this last equation is that the equation may now be solved by taking square roots of both sides...