Determine the Constant That Should Be Added to the Binomial $5 x ^ { 2 } - 2 x - 4 = 0$

Multiple Choice

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
- $5 x ^ { 2 } - 2 x - 4 = 0$

A) $\left\{ \frac { 1 - \sqrt { 21 } } { 5 } , \frac { 1 + \sqrt { 21 } } { 5 } \right\}$
B) $\left\{ \frac { 5 - \sqrt { 21 } } { 25 } , \frac { 5 + \sqrt { 21 } } { 25 } \right\}$
C) $\left\{ - 4 , \frac { 22 } { 5 } \right\}$
D) $\left\{ \frac { - 1 - \sqrt { 21 } } { 5 } , \frac { - 1 + \sqrt { 21 } } { 5 } \right\}$