Sometimes quadratic expressions can be factorised using standard mathematical techniques. However the following method works for all (valid) quadratic expressions. So when in doubt, this technique will work for sure. There are 2 sub techniques applied here: completing the square and difference of squares. Throughout this article we concentrate on the left side (LH) of the expresssion. The Right side is assumed to be 0.

Given variable x and integers a, b, and c, the general LH form of a quadratic expression is

As an example, take the following LH form:

Rework to obtain a quadratic expression starting with x²

Calculate b/2

Square this amount

Add and subtract this amount to the part of the equation in square brackets

Now the first three factors in the square brackets are prepared for factorising. Just use the form

and substitute in the equation:

Using the following form.

In our example, let

and

then

Solving the above gives the solution for the LH expression: