Algebra II Recipe: Completing the Square

1. Set all terms equal to zero.
2. If a ¹ 1, divide all terms by "a".
3. Add or subtract to move the number term to the right.
4. Take half of "b", square it, and add it to both sides.
5. Factor the perfect square trinomial.
• It will always factor into two identical binomials, so write it as (a ± b)².
• "a" is the square root of the first term.
• "b" is the square root of the last term.
• The operation in the binomial will be the same as the operation in front of the "x" term.
6. Add or subtract to move the number on the right to the left and set equal to "y".
7. Multiply both terms on the right by the value of "a" that was divided out in step 2.