Answer:
x = 3 ± 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
given
x² - 6x + 1 = 0 ( subtract 1 from both sides )
x² - 6x = - 1
To complete the square
add (half the coefficient of the x- term)² to both sides
x² - 6x + (- 3)² = - 1 + (- 3)²
x² - 6x + 9 = - 1 + 9
(x - 3)² = 8 ( take the square root of both sides )
x - 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( add 3 to both sides )
x = 3 ± 2[tex]\sqrt{2}[/tex]
