Completing the Square
We can solve quadratic equations like 3x2 = 6 and (x – 2)2 = 7 by using
the principle of square roots. We can also solve an equation such as x2 + 6x + 9 = 2
in like manner because the expression on the left side
is the square of a binomial,(x + 3)2 . This second procedure is the basis for
a method called completing the square. It can be used to solve any quadratic
equation.
Important Notes
When solving an equation, to complete the square of an expression like x2 + bx, we take half the x-coefficient, which is b/2, and square it. Then we add the number, (b/2)2, on both sides of the equation.