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)