Completing the square method.
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
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