To solve the given quadratic equation by completing the square, we first want to work with the equation in a more manageable form. Here are the steps:
1. Start with the given quadratic equation:
[tex]\[ 3x^2 + 9x - 4 = 0 \][/tex]
2. Move the constant term to the right side of the equation:
[tex]\[ 3x^2 + 9x = 4 \][/tex]
3. Factor out the coefficient of [tex]\(x^2\)[/tex] from the left side. The coefficient is 3:
[tex]\[ 3(x^2 + 3x) = 4 \][/tex]
From the above step, we can see that the equation inside the parentheses has been scaled by a factor of 3. So, the value of [tex]\( A \)[/tex] is 3.
Thus, the value of [tex]\( A \)[/tex] is:
[tex]\[ \boxed{3} \][/tex]
