Completing the Square: A Second Example

Step 1

The 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 2

The coefficient of x² is 2, so we divide each term in the equation by 2.

Step 3

The coefficient of the x term is . Dividing by two, and squaring the result gives . The next step is to add to each side.

Step 4

We 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 5

Finally, 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: