Quadratic Equations Online Practice

Question

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7 of 207 of 20 Items

Question
Solve the quadratic equation 46x2−138x=0
by factoring out the GCF.(1 point)
Responses

The solutions are x=0
and x=46
.
The solutions are x equals 0 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=−3
and x=46
.
The solutions are x equals negative 3 and x equals 46 .

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

Answer 1

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

The GCF of the coefficients \( 46 \) and \( -138 \) is \( 46 \). So we can factor \( 46x \) out of the equation:

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

Now we set each factor equal to zero:

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

From the first equation \( 46x = 0 \), we find:

\[ x = 0 \]

From the second equation \( x - 3 = 0 \), we find:

\[ x = 3 \]

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

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

Therefore, the correct response is:

The solutions are \( x = 0 \) and \( x = 3 \).