


Completing the Square: A Second ExampleStep 1The constant term, , is already on the right side. But, we must move to the left side. We do this by adding to each side: Step 2The coefficient of x^{2} is 2, so we divide each term in the equation by 2. Step 3The coefficient of the x term is . Dividing by two, and squaring the result gives . The next step is to add to each side. Step 4We must now factor the left side as a perfect square. As in the previous example, we can assume that the factored form is x plus one half the coefficient of x. Step 5Finally, we take the square root of each side. Then create two subproblems: Subproblem 1: Subproblem 2: And combine the solutions to the subproblems in the solution to the original problem: 

