How to complete the square to solve this problem 3 x 2 = 6 x + 12

Question

How to complete the square to solve this problem   3      x          2        =  6  x  +  12

Raelynn Johnson · Accepted Answer

First we must arrange the problem so it equals zero:

3 x^{2} - 6 x + 12 = 0

Then we move the 12 back to the other side:

3 x^{2} - 6 x = - 12

Now we divide everything by 3 because we need the leadingcoefficient of

x^{2}

to be 1

x^{2} - 2 x = - 4

Now take half of the middle term and then square it and add itto both sides of the equation:

x^{2} - 2 x + 1 = - 4 + 1

Then:

(x - 1)^{2} - 3 = 0

vrteclh · Accepted Answer

First, to solve a quadratic equation in one variable like this one by completing the square, get just the quadratic term and the linear term (if there is one) on one side of the equation. Here, subtract 6x from both sides to get:

3 x^{2} - 6 x = 12

Second, divide each term in the equation by the coefficient of the squared term so its new coefficient is 1.

x^{2} - 2 x = 4

Third, divide the coefficient of the linear term (the x-term) by 2 and square the result.

(- 2 / 2)^{2} = 1

Then add this number to both sides. Now you have:

x^{2} - 2 x + 1 = 4 + 1

Fourth, simplify the right side:

x^{2} - 2 x + 1 = 5

or

x^{2} - 2 x - 4 = 0

how to complete the square to solve this problem 3x^2 = 6x + 12

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