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} = a^{2} + 2ab + b^{2}

(a – b)^{2} = a^{2} – 2ab + b^{2}

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:

a^{2} – 6a – 12 = 0

This is a standard quadratic equation. To make it so that it represents the square of two expressions, you ...

Start Free Trial

No credit card required