Working with the basic form of the quadratic equation the previous section afforded, you gain some sense of what it is to complete the square of an expression to solve a quadratic equation. For starters, recall that these two equations represent standard forms of polynomials that incorporate squares:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
Generally, completing the square begins with examining an equation to discover whether you can rewrite it in a way that allows you to make a perfect square on the left side of the equal sign. To understand how this works, consider the following equation:
a2 – 6a – 12 = 0
This is a standard quadratic equation. To make it so that it represents the square of two expressions, you ...