1. ## completing square

dear,

anybody knws how is the easiest way to completing square? or a more simple way?
ex : x^2 - 4x - 5 = 0

thank you

2. Note that if you expand $(x + a)^2$ you get $x^2 + 2ax + a^2$. Now look at the 'a' value in the 2ax term. That is your 'a' value in the $(x + a)^2$ expression.

So if you have a equation such as $x^2 + 6x + 6$... This can be re-written as $x^2 + 2 \cdot 3x + 6$ and hence 3 is your 'a' value. So in this example completing the square would be...

$x^2 + 6x + 6 = (x + 3)^2 - 3$ since expanding $(x + 3)^2$ gives $x^2 + 6x + 9$ so you need to take away a 3 from it to match your original equation.

Basically to generalize... If you have an equation of the form $x^2 + nx + m$ where n and m are some numbers, you should divide n by 2 to get the 'a' value in the equation $(x + a)^2$.

$x^2 - 4x - 5 = 0$
Your n value is -4. Divide this by 2 to get -2. This is your 'a' value. Put this into the equation $(x + a)^2$ to get... $(x - 2)^2$.

Now expand this... $(x - 2)^2 = x^2 - 4x + 4$. Since this is different from you original equation you need to subtract 9 to turn the +4 into a -9...

So your answer is! $(x - 2)^2 - 9$.

3. ## Completing the Square

Hello janeyandtaz
Originally Posted by janeyandtaz
dear,

anybody knws how is the easiest way to completing square? or a more simple way?
ex : x^2 - 4x - 5 = 0

thank you
Completing the square is a bit tricky to explain, but you may find you can follow the technique I've described here, where I've broken it down to 6 steps in my answer to Question 1. (You'll see that I've given an example where the coefficient of $x$ is not equal to $1$.)