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

Question

Solve the quadratic equation  46x2−138x=0  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=−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=0 and x=46.

GPT-4o mini · Answer

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. 1. The GCF of $46x^2$ and $-138x$ is $46x$. 2. We can factor out $46x$ from the equation: $$ 46x(x - 3) = 0 $$ 3. Now we can set each factor equal to zero: $$ 46x = 0 \quad \text{or} \quad x - 3 = 0 $$ 4. Solving these gives us: - From $46x = 0$: $$ x = 0 $$ - From $x - 3 = 0$: $$ x = 3 $$ Thus, the solutions to the equation are $x = 0$ and $x = 3$. The correct response is: The solutions are $x = 0$ and $x = 3$.