Solve the quadratic equation 46x2−138x=0

Question

by factoring out the GCF.(1 point)
Responses

The solutions are x=0
and x=3
.
The solutions are x is equal to 0 and x is equal to 3. - no response given

The solutions are x=−46
and x=3
.
The solutions are x is equal to negative 46 and x is equal to 3. - no response given

The solutions are x=0
and x=46
.
The solutions are x is equal to 0 and x is equal to 46. - no response given

The solutions are x=−3
and x=46
.
The solutions are x is equal to negative 3 and x is equal to 46. - incorrect
Incorrect

Factor out the GCF and then solve by setting each factor equal to zero.
Remaining Attempts : 1
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Answer 1

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

1. The GCF of \(46x^2\) and \(138x\) is \(46x\).

2. Factoring out \(46x\) from the equation: \[ 46x(x - 3) = 0 \]

3. Now, we set each factor equal to zero:

   • First factor: \[ 46x = 0 \implies x = 0 \]
   • Second factor: \[ x - 3 = 0 \implies x = 3 \]

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

• \(x = 0\)
• \(x = 3\)

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