## Thursday, 29 March 2012

### Quadratic - completing the square

Completing the square is a technique to solve Quadratic Equation.
Key questions to ask when using this technique are:
• What is Completing the Square technique?
• Why do we use Completing the Square?
• When is it used?
• How is the Completing the Square technique applied?
The following resources will be used to aid your understanding of the topic on Completing the Square.

Resource 1
Media and Video

Video 1

Video 2: Fundamental

video 3: summary and song

Resource 2

ACE Learning
The link is shown as follows:

Resource 3
Worksheet 3 for notes, worked examples and practice questions.

1. When to use 'Completing The Square':
For your average everyday quadratic, you first have to use the technique of "completing the square" to rearrange the quadratic into the neat "(squared part) equals (a number)" format.

Group Members: Kang Xiong,Ada,Yong Jie,Bryan,Teri and Jasmine.

2. Completing the square can basically find out the answer of an quadratic equation.
For example:
x^2 + 6x + 5 = 0
Then,
(x+3)^2 - 4=0
So,
(x=3)^2=4
Then,
x+3 = -2 or x+3 = 2
Thus,
x = -5 or x= -1

That is why completing the square is important, because it can find out any quadratic equation
(grp members: Boon Pin, Sylvia Soh, Gavin Chong and Kaneko Yoshiki) sorry i forgot to sign out of this account

3. How is the Completing the Square technique applied?

Let the equation be x^2+8x=20

Step 1) Separate the quadratic from the constant term. Ensure that the coefficient of x^2 is 1.

Step 2) Add half the coefficient of 8x and remove the x, then square it, therefore add (8/2)^2 to both sides of the equation.

Step 3) Simplify the equation, resulting in x^2+8x+(4)^2=20+(4)^2

Step 4) Factorise the left side of the equation. (x+4)^2 = 36

Step 5) Remove the square, therefore square root both sides of the equation. Remember that you have a positive and negative square root.

Step 6) Express as 2 integers answers

4. What us Completing the Square technique?

It is a technique to factorise the general form of quadratic equations, which is ax^2 + bx + c = 0
In mathematics, completing the square is considered a basic algebraic operation, and is often applied without remark in any computation involving quadratic polynomials.
This method works when the coefficient is 1. If the coefficient is higher than 1, just divide it to get 1.
This is a more simplified method for factorization.