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