Quadratic Equation (2)

We have discuss the method of factorization to find the roots of a quadratic equation. Now we will study the completing square method.

As depicted by its name, this procedure use a complete square form. Suppose we want to find the roots of the quadratic equation

STEP ONE : First move the constant to the right hand side of the equation.

STEP TWO : Divide both sides with 2. We have this form of equation

Note : 2 is the coefficient of x square or a. You may have another value of a. Just divide both sides with a.

STEP THREE : Then we add both sides with the square of half of the x’s coefficient. In this example, the coefficient of x is 2. One half of 2 is 1. The square of 1 is still 1. So we add both sides with 1 to have the following equation.

The left hand sides is a complete square form.

STEP FOUR : Then we can rewrite is as a square of something, have a look.

STEP FIVE : Take the square root of both sides.

STEP SIX : Isolate the x to find the roots of the equation.

This is how the completing square method works. This method is stronger than the factorization method. But it is a little bit tedious. We can use this method to find the roots of all quadratic equations. If a equal to one, then we can skip step two.

I have some examples and exercises. You can download them by click the following link.

Quadratic Equation, the completing square method.