Place the following steps in order to complete the square and solve the quadratic equation, x^2 - 6x + 7 = 0

We have the following equation:

x ^ 2 - 6x + 7 = 0

Step 1:

Pass the constant term to the right:

x ^ 2 - 6x = - 7

Step 2:

Add (b / 2) ^ 2 to both sides of the equation:

x ^ 2 - 6x + (-6/2) ^ 2 = - 7 + (-6/2) ^ 2

x ^ 2 - 6x + (-3) ^ 2 = - 7 + (-3) ^ 2

x ^ 2 - 6x + 9 = - 7 + 9

x ^ 2 - 6x + 9 = 2

Step 3:

Rewrite polynomial:

(x-3) ^ 2 = 2

Step 4:

Clear x:

x-3 = + / - root (2)

The solutions are:

x1 = 3 + root (2)

x2 = 3 - root (2)

Answer:

x1 = 3 + root (2)

x2 = 3 - root (2)