This is one of the trickiest things you have to do. Basically you have to express a quadratic as a squared bracket with a number on the end to ‘complete it’…confused…then read on.
What You Need To Do
- Arrange the quadratic in the standard form ax2 + bx + c = 0
- Write out a bracket as (x + b/2)2
- Multiply out the brackets and compare to the original quadratic
- Add or subtract the difference
- Solve the equation
Example: Take x2 + 6x – 7 = 0
Write out the squared bracket and multiply it out
(x + 3)2 = x2 + 6x + 9
So to make this like the original you need to minus 16 from both sides (to get from +9 to -7). So the completed square is:
(x + 3)2 – 16 = 0
You might be asked to solve it…which is now quite easy.
(x + 3)2 = 16
Therefore x + 3 = ±4
Therefore x = ±4 – 3
Therefore x = 1 or x = -7