Question

sienna is solving the quadratic equation by completing the square.
$3x^2 + 9x - 4 = 0$
$3x^2 + 9x = 4$
$a(x^2 + 3x) = 4$
what is the value of $a$?
$\circ -4$
$\circ -3$
$\circ 3$
$\circ 4$

Explanation:

Step1: Analyze the equation

We have the equation \(3x^{2}+9x = 4\) and we want to write it in the form \(A(x^{2}+3x)=4\).

Step2: Factor out A from the left - hand side

If we factor out a common factor from \(3x^{2}+9x\), we know that \(3x^{2}+9x=3(x^{2} + 3x)\) (since \(3\times x^{2}=3x^{2}\) and \(3\times3x = 9x\)). Comparing with \(A(x^{2}+3x)=4\), we can see that \(A = 3\).

Answer:

3