1. Identify the coefficient of ( x ):
The given expression is ( x² - 8x + 1 \). The coefficient of ( x ) is (-8).
2. Divide the coefficient of ( x ) by 2 and square it:
[tex]\left(\frac{-8}{2}\right)^2 = (-4)^2 = 16[/tex]
3. Add and subtract this square inside the expression:
[tex]x^2 - 8x + 16 - 16 + 1[/tex]
4. Rewrite the expression:
Group the perfect square trinomial and the constants separately:
[tex] (x^2 - 8x + 16) - 16 + 1[/tex]
5. Factor the perfect square trinomial:
[tex] (x - 4)^2 - 15[/tex]
The expression ( x² - 8x + 1 ) can be rewritten by completing the square as:
[tex](x - 4)^2 - 15[/tex]
