Understanding Completing the Square

I obviously understand HOW to complete the square but what I'm very curious about is "why" the steps associated with completing the square is carried out. For example, how does halfing the value of the coefficient of x and then squaring it makes the quadratic a perfect square?

Somebody please explain because, as a maths student, the only aspect of my weakness is the inability to understand how and why steps are carried out in maths in order to reach a certain solution.

If somebody could help me understand this, I'll very much appreciate it as my AS maths exam is tomorrow!! :frown:

Thank you!

Reply 1

2710

18

In certain situations where you cannot factorise, you can either use the formula or complete the square. And completing the square is just faster. That's why I use it anyways :P

And in some questions completing the square is needed, such as integration.

Reply 2

harryhorse3

A quadratic equation is y=ax2+bx+c
(dont know how to do superscript 2 for squared on this)
Generally when completing the square, "a" will be a n integer which has an integer root.
By halfing the coefficient of x, you then end up with

(rootax=0.5b)2 whn this is multiplied out it gives ax2+bx+d.
What needs to be done then is -d to remove this added value. so finally:
y=(rootax+0.5b)2 +c-d

soz about the word root and the big 2

Reply 3

2710

18

Yeh, like this:

x^2 -10x + 11

(x - 5)^2 + 11 - 25

You minus the 25, since if you break out the brackets, you've got an extra 25, this will be equivalent to the first line, but this is much easier to manipulate

Reply 4

Joy Division

14

sonya_x

I obviously understand HOW to complete the square but what I'm very curious about is "why" the steps associated with completing the square is carried out. For example, how does halfing the value of the coefficient of x and then squaring it makes the quadratic a perfect square?

Somebody please explain because, as a maths student, the only aspect of my weakness is the inability to understand how and why steps are carried out in maths in order to reach a certain solution.

If somebody could help me understand this, I'll very much appreciate it as my AS maths exam is tomorrow!! :frown:

Thank you!

because

(x+a)^2 = x^2+2ax+a^2

this is true for any value of a

Understanding Completing the Square

Related discussions

Latest

Trending

Trending

Articles for you