The method that you have given is similar to completing the square, but it has variations that I am not familiar with. I will do my best to explain what is meant by each step along with showing what the equation should look like

We begin with x^{2} + 12x - 64 = 0

1. The first step says to "move" the constant term to the right side of the equation. This means that we will add 64 for to each side so that there will be a constant on the right side, but no constant on the left.

The new equation will be x^{2 }+ 12x = 64.

2. The second step says to multiply each term in the equation by four times the coefficient of the x^{2} . The coefficient of the x^{2} term is 1, so we are going to multiply each term by 1 times 4. 1 times 4 is 4, so we will multiply each term by 4.

The new equation will be 4x^{2} + 48x = 256.

3. The third step says that we need to square the original coefficient of the x term and add it to both sides. The original coefficient of the x term is 12. When I square 12, I get 144. I need to add 144 to both sides. I then need to simplify the right side (add 256 and 144 to get 400)

The new equation will be 4x^{2} + 48x + 144 = 400

4. The fourth step says to take the square root of both sides. Before you do this, you should factor the left side into a square term. This means that you will come up with two identical factors for the term on the left. The coefficient of the x term of the factor will be the square root of your x^{2} factor, while the constant term of the factor will be the square root of your constant. In this case, the coefficient on the x term of the factor will be 2 (the square root of 4) and the constant term will be 12 (the square root of 144).

The factored version from step 3 will be (2x + 12)^{2} = 400. If you want to double check this, foil the two factors and see if you get the correct quadratic.

After you find the square factor of the quadratic on the left, take the square root of both sides, but remember that you want the positive and negative square roots on the right. Your left hand term will be the factor inside parenthesis.

The new equations (there are two of them now) are 2x + 12 = 20 and 2x + 12 = -20.

5. We are going to solve the first equation in this step. Solve 2x + 12 = 20 by subtracting 12 from each side and then dividing by 2. The answer should be 4.

6. Finish by solving 2x + 12 = -20. First subtract 12 from each side, then divide each side by 2. The answer will be -16.

## Comments

awesome, thanks!