Completing the Square

Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .

To solve by completing the square:

      1.  Transform the equation so that the constant term, , is alone on the right side.
      2.  If , the leading coefficient (the coefficient of the term), is not equal to , divide both sides by .

      3.  Add the square of half the coefficient of the -term, to both sides of the equation.

      4.  Factor the left side as the square of a binomial.

      5.  Take the square root of both sides.  (Remember: is equivalent to .)

      6.  Solve for .