Solve the quadratic equation 46x2−138x=0

Question

by factoring out the GCF.(1 point)
Responses

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

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=46
.

Answer 1

To solve the quadratic equation \(46x^2 - 138x = 0\) by factoring out the greatest common factor (GCF), follow these steps:

1. Identify the GCF of the terms in the equation. The GCF of \(46x^2\) and \(-138x\) is \(46x\).

2. Factor out the GCF: \[ 46x(x - 3) = 0 \]

3. Set each factor equal to zero: \[ 46x = 0 \quad \text{or} \quad x - 3 = 0 \]

4. Solve for \(x\):

   • From \(46x = 0\): \[ x = 0 \]
   • From \(x - 3 = 0\): \[ x = 3 \]

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

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