Factor by completing the square x2-2x-168

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

(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)