How would you solve x^2 - 6x + 7=0 to complete the square and solve the quadratic equation?

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