When completing the square, the lead coefficient should be one.  To achieve this, divide both sides of the equation by the coefficient of the squared term.

and

This leaves you with the equation 

a. Once the variables are on the left, the constant is on the right, and the lead coefficient is 1, you will create a perfect square trinomial on the left side of the equation.  Do this by starting with the coefficient of the x term.

b. Divide this by 2.

c. Square this term.

d. Add the result to both sides of the equation.

e.  The expression on the left side of the equation is now a perfect square trinomial and can be factored to:

a. Take the square root of both sides.  Don't forget to account for both positive and negative answers.

b. Simplify both sides

c. Isolate the variable by adding 5/4 to both sides.

a. Once the variables are on the left side of the equation and the constant is on the right, make the lead coefficient 1 by dividing both sides of the equation by the coefficient of the squared term.

b. Simplify

To complete the square, you must create a perfect square trinomial on the left side of the equation. 

a. Take the square root of both sides.  Don't forget to account for both positive and negative answers.

b. Simplify both sides, if possible.

c. Isolate the variable by subtracting 2 from both sides.

To complete the square, we need to have the x terms on one side and the numbers on the other. Therefore,

becomes 

When we want to complete the square, we want an equation in the form  or  so that we can factor it into  or . To do this, we take half of the numeric portion of what we want our b term to be (in this problem ) and square it, therefore:

Therefore, we add 16 to each side to obtain:

 and 

To complete the square, we need the left side in a form  or  so that we can factor it into form  or .

To do this, we first divide out three on the left-hand side to obtain:

We then take 1/2 of the number in our  term (in this case ) to obtain :

We then must add this to each side, but because we are completing the square inside of a parenthesis which is being multiplied by 3, we don't add 36 to each side, but rather 3 times 36, or 108. Therefore, we obtain:

 and 

Once the polynominal is factored out and everything is moved to the left, the equation becomes  which does not factor evenly, so you could use the quadratic formula, or complete the square. To complete the square, a coefficient must be found to factor the polynominal into a perfect square. The polynominal  factors to  so we know that  so  and . To complete the square you add and subtract  from the left side of the equation and strategically place parentheses to get , this simplifies to , which simplifies to , 

When using the complete the square method we will divide the  coefficient by two and then square it. This will become our  term which we will add to both sides.

In the form,

our ,  and we will complete the square to find the  value. 

Therefore we get: