Solve the quadratic equation 46x^2−138x=0

Question

by factoring out the GCF.(1 point)
Responses

The solutions are x=0 and x=46

The solutions are x=0 and x=3
The solutions are x=−3 and x=46
The solutions are x=−46 and x=3

Answer 1

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

The GCF of \( 46x^2 \) and \( -138x \) is \( 46x \). We can factor out \( 46x \):

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

Next, we set each factor equal to zero:

1. \( 46x = 0 \)
2. \( x - 3 = 0 \)

From \( 46x = 0 \):

\[ x = 0 \]

From \( x - 3 = 0 \):

\[ x = 3 \]

Thus, the solutions are \( x = 0 \) and \( x = 3 \).

Therefore, the correct response is:

The solutions are x=0 and x=3.