Solve for v.

(v-1) ^2 = 2v^2 - 5v - 17

If can be more than one solution or no solution

(v - 1) ² = 2v² - 5v - 17

(v - 2) (v - 2) = 2v² - 5v - 17

v² - 2v - 2v + 4 = 2v² - 5v - 17

v² - 4v + 4 = 2v² - 5v - 17

- v² - v²

-4v + 4 = v² - 5v - 17

+ 5v + 5v

v + 4 = v² - 17

+ 17 + 17

v + 21 = v²

0 = v² + v + 21

v² + v + 21 = 0

v = - (1) + / - √ ((1) ² - 4 (1) (21))

2 (1)

v = - 1 + / - √ (1 - 84)

2

v = - 1 + / - √ (-83)

2

v = - 1 + / - 9.11i

2

v = - 1 + 4.555i

v = - 1 + 4.555i v = - 1 - 4.555i

There is more than one solution.