The justification of step a is common denominator and the justification of step b is multiplication property of equality
The equation is given as:
[tex]a(x + \frac{b}{2a})^2 = -c + \frac{b^2}{4a}[/tex]
Take the LCM
This gives
[tex]a(x + \frac{b}{2a})^2 = \frac{-4ac + b^2}{4a}[/tex]
The above represents a common denominator.
Multiply both sides by 4a
[tex]4a^2(x + \frac{b}{2a})^2 = -4ac + b^2[/tex]
The above represents the multiplication property
Hence, the justifications are common denominator and multiplication property of equality
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