Solving Quadratic Equations using the Quadratic Formula

How do you find solutions i.e the x value(s) in quadratic equations. There are several methods of finding quadratic solutions:

• Simple factorisation
• Completing the Square
• Quadratic Formula
• Graphical methods

Quadratic equations are of the form ax@2 + bx + c
Here's a simple Quadratic equation and will use simple factorisation:

	x@2 - 5x + 6 = 0
	x@2 -3x -2x = 0
	x(x - 3) -2(x - 3) = 0
	(x - 3)(x - 2) = 0
	Solve the equation
	x - 3 = 0 or x - 2 =0
	x = 3 or x = 2

Simple factorisation works where simple terms can be found such that when you add two numbers you get the middle term and multiple you get the last term.

However, what if common factors cannot be found, for example:
2x@2 - 9x + 10, x@2 - 19x - 22
The Quadratic formula deals with such equations

Factorise 2x@2- 9x + 10

Here we substitute a, b, c with their respective constants:

a =2, b= 9, c= 10