Completing The Square

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)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)– 16 = 0

You might be asked to solve it…which is now quite easy.

(x + 3)= 16

Therefore x + 3 = ±4

Therefore x = ±4 – 3

Therefore x = 1 or x = -7