The sum of the roots of 8x² - 2x = 1 is:

-1/4

1/4

-1/8

8x^2-2x-1=0

8x^2-4x+2x-1=0

4x (2x-1) + 1 (2x-1) = 0

(4x+1) (2x-1) = 0

x=1/2 and - 1/4

So the sum is 1/2-1/4=1/4

1/4

8x^2 - 2x = 1

8x^2 - 2x - 1 = 0

(2 + / - √ (-2) ^2 - 4 (8) (-1)) / 2 (8)

(2 + / - √4 + 32) / 16

(2 + / - √36) / 16

(2 + / - 6) / 16

2+6/16

1/2

2-6/16

-1/4

now since they want the sum of the roots

1/2 - 1/4

sum = 1/4