Answer is (x - 4)^2 + 6
Step by step
Your equation
x^2 -8x + 22=0
Isolate the constant to the right of =
x^2 -8x = -22
Divide the coefficient of x by 2 and square it, then add that to both sides
-8/2 = -4
-4^2 = 16
x^2 -8x +16 = -22 + 16
Simplify
x^2 -8x + 16 = -6
Factor the left side. What number added together is sum of -8 and squared is product of 16? Answer is -4.
(x - 4) ^2 = -6
Move “b” to join the left side to answer in the form of (x-a)^2 + b
your answer
(x - 4)^2 + 6