Question

Solve the quadratic equation 46x^2 - 138x = 0 by factoring out the GCF.

Answer 1

To solve the quadratic equation \( 46x^2 - 138x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms.

The two terms are \( 46x^2 \) and \( -138x \). The GCF of the coefficients \( 46 \) and \( -138 \) is \( 46 \), and both terms contain at least one \( x \). Therefore, the GCF is \( 46x \).

Now we can factor out \( 46x \) from the equation:

\[
46x^2 - 138x = 46x(x - 3) = 0
\]

Now we have the factored equation:

\[
46x(x - 3) = 0
\]

Next, we set each factor to zero to find the solutions:

1. \( 46x = 0 \)
\[
x = 0
\]

2. \( x - 3 = 0 \)
\[
x = 3
\]

Therefore, the solutions to the equation \( 46x^2 - 138x = 0 \) are:

\[
x = 0 \quad \text{and} \quad x = 3
\]