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Sienna is solving the quadratic equation by completing the square.

[tex]\[
\begin{array}{r}
3x^2 + 9x - 4 = 0 \\
3x^2 + 9x = 4 \\
A(x^2 + 3x) = 4
\end{array}
\][/tex]

What is the value of [tex]\( A \)[/tex]?

A. [tex]\(-4\)[/tex]

B. [tex]\(-3\)[/tex]

C. [tex]\(3\)[/tex]

D. [tex]\(4\)[/tex]

Sagot :

GinnyAnsweridn
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]
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