Completing the square is a way to simplify polynomial expressions by writing them as sums or differences of squares. The method goes like this:

  1. Starting with an expression such as this:
    Ax2 + Bx + C
  2. Divide through by A so that the x2 term has a coefficent of 1.
    x2 + (B / A)x + (C / A)
  3. Add and subtract one half (B / A) squared.
    x2 + (B / A)x + (B / (2A))2 + (C / A) - (B / (2A))2
  4. The first three terms of the above expression can be written as
    (x + (B / (2A)))2
    This can be verified by multiplying the expression out.
  5. The finished formula can be written as
    (x + (B / (2A)))2 + (C / A) - (B / (2A))2
  6. Multiplying out the last two terms gives us a total result of:
    (x + (B / (2A)))2 + (4AC - B2) / (4A2)

Log in or registerto write something here or to contact authors.