Question

Factor by completing the square x2-2x-168

Answer 1

y=x^2-2x-168
y+168=x^2-2x
y+169=x^2-2x+1
y+169=(x-1)^2
y=(x-1)^2-169

Answer 2

(x+a)^2 = x^2 +2ax+a^2

x^2-2x-168

x^2-2x                                      -168
"complete" the square

x^2 -2x +(1^2)                           -168 -(1^2)

factor

(x-1)^2 -169

this is a difference of squares
(x-1)^2 -13^2

a^2 -b^2= (a+b)(a-b)

((x-1)+13)((x-1)-13)

=
(x+12)(x-14)