Question

atraeus is solving the quadratic equation by completing the square.
$7x^2 - 14x + 6 = 0$
$7x^2 - 14x = -6$
$a(x^2 - 2x) = -6$
what is the value of $a$?
$\circ$ $-14$
$\circ$ $2$
$\circ$ $6$
$\circ$ $7$

Explanation:

Step1: Analyze the equation transformation

We have the equation \(7x^{2}-14x=-6\) and it is transformed to \(A(x^{2}-2x)=-6\). We need to find the value of \(A\) such that \(7x^{2}-14x = A(x^{2}-2x)\).

Step2: Factor out the common term

Notice that \(7x^{2}-14x\) can be factored as \(7(x^{2}-2x)\) (by factoring out the greatest common factor of \(7x^{2}\) and \(- 14x\), which is \(7\)). So comparing \(7(x^{2}-2x)\) with \(A(x^{2}-2x)\), we can see that \(A = 7\).

Answer:

\(7\) (corresponding to the option: \(7\))