Write X^2-6x+1 in the form (x+a)^2+b?

x² - 6x + 1
= (x² - 6x) + 1
= (x² - 2*x*3 + 3²) + 1 - 3²
= (x - 3)² - 8
= [x + (-3)]² + (-8)

x^2-6x+1
=
x^2-6x+3^2-3^2+1
=
(x-3)^2-8
=>
a=3
b=-8

x^2 - 6x + 1
= (x - 3)^2 - 8

x^2 - 6x + 1
= (x - 3)^2 - 8

Complete the square.
x^2 - 6x + 1 =
x^2 - 6x + (6/2)^2 + 1 - (6/2)^2 =
(x - 3)^2 + 1 - 9 =
(x - 3)^2 - 8

Complete the square:
x² - 6x + 1
= (x² - 6x) + 1
= (x² - 6x + 9) - 9 + 1
= (x-3)² - 8

Here's how I do it.  Similar process, but I think a little more streamlined.

You are asked to put that quadratic into vertex form.  I'll set the expression to a variable so we have an equation, then we need to get the right side of that equation into the form of (x² + bx).  We can do that by subtracting 1 from both sides:

y = x² - 6x + 1
y - 1 = x² - 6x

Now we complete the square by adding 9 to both sides:\

y + 8 = x² - 6x + 9

The right side now factors:

y + 8 = (x - 3)²

Now solve for y again:

y = (x - 3)² - 8