What is completing the square and how do you do it?
Completing the square is just another way of solving a quadratic equation; It is useful if you cannot factorise the equation.
When completing the square you want to end up with your equation in the format:
(x+1)2-1=0
So let's try it with an example:
9x2+6x-5=0
The first thing to do is to find our square.
We only need 9x2+6x for this.
Now we square root the coefficient of x2 which in this case is 9, so we get 3.
So now we know our square looks like this:
(3x+?)2
To find our question mark we need to take the coefficient of x, halve it and then divide it by our first number (3) , so our example is 6 becomes 1.
6/2=3
3/3=1
So this gives us our square:
(3x+1)2
Now to make it add up we square our second number (1) and take the result away from our square:
(3x+1)2 -1
Now we need to make this match our original equation, we had -5 on the end of our equation so we add that on:
(3x+1)2 -1-5
Giving us our answer:
(3x+1)2 -6=0
Now to find the value of x we take 6 to the other side of the equation:
(3x+1)2 =6
And then square root the equation:
3x+1= + or - sqrt(6)
After that we take away the one and divide by 3 giving us the answer:
x=(sqrt(6)-1)/3 or (-sqrt(6)-1)/3
