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 in the equation.

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

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

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

Next, we set each factor equal to zero and solve for \(x\):

1. Setting the first factor equal to zero:
\[
46x = 0
\]
Dividing both sides by 46:
\[
x = 0
\]

2. Setting the second factor equal to zero:
\[
x - 3 = 0
\]
Adding 3 to both sides:
\[
x = 3
\]

Thus, the solutions to the quadratic equation \(46x^2 - 138x = 0\) are:
\[
x = 0 \quad \text{and} \quad x = 3
\]