Completing the square
Revision as of 15:22, 17 June 2006 by PenguinIntegral (talk | contribs)
Motivations
Quadratic equations are usally hard to solve, if they do not factor.
Some of them, in forms 
, are easy to solve by taking the squareroot of b and subracting a. Completing the square is a technique to munipulate every quadratic into the easily solve-able form above.
General Solution For A Monic Quadratic
Let the quadratic be in the form 
.
Moving be to the other side, we obtain
Then, adding a^2/4 to each side and factoring, we get
Which is solvable as described above.
Applications of Adding and Factoring
Other degrees of polynomials may be solved by adding constant terms and factoring.
