Question

The method of completing the square was used tosolve the equation 2x² – 12x+6= 0. Whichequation is a correct step when using this method?1) (x - 3)2 = 62) (x - 3)2 = -63) (x - 3)2 = 34) (x - 3)2 = -3

Answer 1

In order to complete the square, we need to write the given equation (2x² - 12x + 6 = 0) in the form:

(x - d)² = f

So, to find the constants d and f, let's expand the above general form:

(x - d)² = f

x² - 2dx + d² = f

x² - 2dx + d² - f = 0

Now, we need to identify d and f by comparing the last equation with the given one. First, though, to make it easier to compare them, let's divide both sides of the given equation by 2:

x² - 6x + 3 = 0

x² - 2dx + d² - f = 0

Then, we have:

2d = 6

d = 3

d² - f = 3

3² - f = 3

9 - 3 = f

f = 6

Thus, using the method of completing the square, we obtain the equation:

(x - d)² = f

(x - 3)² = 6

Therefore, option 1) is correct.