ANSWER
C. Factoring a perfect square trinomial.
EXPLANATION
The first step shown is:
[tex] {x}^{2} + \frac{b}{a}x + ( \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]
Observe that the left hand side is a perfect square trinomial.
In other words, the left hand side is of the form,
[tex] {m}^{2} + 2mn + {n}^{2} [/tex]
which can be factored as:
[tex] {m}^{2} + 2mn + {n}^{2} = {(m + n)}^{2} [/tex]
When we factor the perfect square trinomial on the left hand side, we obtain:
[tex]( x + \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]
The correct answer is C
