# Quadratic Equations

Quadratic equations can be solved by factorising, completing the square and using a formula. In this section you will learn how to:

- solve quadratic equations by factorising
- solve quadratic equations by completing the square
- solve quadratic equations by using the formula
- solve simultaneous equations when one of them is quadratic

**Solving quadratic equations by factorising**

Unless a graphical method is asked for, quadratic equations on the non-calculator paper will probably involve factorising or completion of the square. Quadratic equations can have two different solutions or **roots**.

You may need a quick look at 'factorising' again to remind yourself how to factorise expressions such as:

x2 − x − 6

which factorises into (x − 3)(x + 2),

a^{2} − 3a

which factorises into a(a − 3)

and

b^{2} − 2b + 1

which will factorise into (b − 1)^{2}.

This video shows you how to solve a quadratic equation by factoring.

**Solving quadratic equations by completing the square**

**NOTE: Check by substituting both roots back into the original equation.**

*This following is a common way to lead into asking you to use completion of the square.*

**NOTE: Remember in, for example, (x + n) ^{2} the number of xs (called the coefficient of x) is 2_{n}. So the coefficient of x will be 6 in (x + 3)^{2}.**

**Solving quadratic equations by using the formula**

When using the quadratic formula, don’t forget the ‘*2a*’denominator. Also, be careful when dealing with negative numbers

inside the square root. State your values of *a,b* and *c* to be used in the formula.

**NOTE: The above calculations are easily checked − especially if your calculator can store numbers as variables.**