The correct answers are x = 7 and x = -1.
In order to complete the square, you have to complete a process by which we make the equation a perfect square. To do this we need to follow the steps below.
x^2 - 6x + 7 = 0
Start by subtracting the constant away from the left side.
x^2 - 6x = 7
Now take half of the x term's coefficient and square it. Then you can add that to both sides. The x terms coefficient is -6. Half of that is -3. Then -3 squared is 9. So we add 9 to both sides.
x^2 - 6x + 9 = 16
Now the left side is a perfect square.
(x - 3)^2 = 16
Now we can subtract the coefficient back to the left.
(x - 3)^2 - 16 = 0
