which equation has same equation as x2 - 6x - 12 = 0

Question

option 1: (x+3)² = 21

option 2: (x-3)²=21

option 3: (x+3)²=3

option 4: (x-3)²=3

I did the box method and now im just confused because none of the equations gave me x2 - 6x - 12 = 0

Answer 1

If you have not been taught how to complete the square yet then you should be able to take each answer and multiply it out to get your equation. I am assuming that you either tried the box method to factor the trinomial and you discovered that there are no factors of -12 that subtract to equal -6. Or maybe you used the box method to multiply out each one and you were left feeling like none of the answers matched your equation. However you can get the correct answer this way. The answer is option 2.

(x -3)(x-3) = 21

x² -6x + 9 = 21

-21 -21

x² - 6x -12 = 0

Answer 2

Start with the given equation: x² - 6x - 12 = 0

Add 12 on both sides:

x² - 6x - 12 + 12 = 0 + 12

x² - 6x = 12

Now to complete the square, add 9 on both sides

x² - 6x + 9 = 12 + 9

x² - 6x + 9 = 21

Using the formula (a - b)² = a² - 2ab + b², (in our case a = x, b = 3) we can write

(x - 3)² = 21

So, the answer is option 2.