Solve the quadratic equation 46x2−138x=0

Question

by factoring out the GCF.(1 point)
Responses

The solutions are x=−3
and x=46
.
The solutions are x equals negative 3 and x equals 46 .

The solutions are x=0
and x=3
.
The solutions are x equals 0 and x equals 3 .

The solutions are x=−46
and x=3
.
The solutions are x equals negative 46 and x equals 3 .

The solutions are x=0
and x=46
.

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 in the equation.

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

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

Now, we can set each factor equal to zero:

1. \( 46x = 0 \)

   • Dividing both sides by 46 gives: \[ x = 0 \]

2. \( x - 3 = 0 \)

   • Adding 3 to both sides gives: \[ x = 3 \]

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

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

The correct response is: The solutions are \( x = 0 \) and \( x = 3 \).