Completing the square!

Rearrange the quadratic into standard form: ax² + ab + c = 0

If 'a' is not 1 then divide everything by a to make it 1.

Ignore the '+ c' for the moment and just put 'ax² + ab' into brackets like so:

(a+b/2)² Remember to divide 'b' by 2

Multiply the brackets out, and compare the original to find out what extra is needed to add or subtract from the existing amount.

x²- 6x - 7 = 0

'a' already = 1 so we go straight to the next step

ignore the '-7' and put the x²- 6x into brackets

(x - 3)²= 0

expand this out

(x - 3)(x - 3) = 0   x²- 3x - 3x + 9 = 0

simplify

x²- 6x + 9 =0

find the diffrence between this and the original

x² - 6x + 9 - x²- 6x -7 = -16

So to compleate the square we write (x - 3)²- 16 = 0