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Firstly you check to see if there is a coefficient to the x² term, in this example there isn't so we know that both the brackets will have a single x in, (x +  )(x +  ). We also know both the s...

We know that to complete the square we put the equation in the form (ax+b)^2+c=0. So we must do that to our equation.

We will begin by establishing what will be within our squared brackets. As ther...

aw + 3 = 4(bw + 5)    Let's get rid of those brackets...
aw + 3 = 4bw + 20    Now we rearrange...
aw - 4bw = 17        Factorise...
w(a - 4b) = 17        Final rearrange...
w = 17 ...

Let's say we have the equation y = 2x + c and we are told that the line passes through the point (3, 4).  Our first step is to use the numbers from the point (3, 4), by substituting them into our equation...

From first principles: ax10^4 is the same as a0000. ax10^2 is the same as a00

So, a0000

          a00

     a0a00

If we look at this pattern and compare to the number in ...