Solve the quadratic equation 46x^2-138x=0 by

Question

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.

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

Next, we factor out \( 46x \):

\[ 46x^2 - 138x = 46x(x - 3) \]

Now, we set the factored expression equal to zero:

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

Next, we can use the zero product property, which states that if the product of two factors is zero, at least one of the factors must be zero. Thus, we set each factor equal to zero:

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

Solving these equations:

1. From \( 46x = 0 \): \[ x = 0 \]

2. From \( x - 3 = 0 \): \[ x = 3 \]

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

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

Answer 2

shorter please

Answer 3

To solve the quadratic equation \( 46x^2 - 138x = 0 \) by factoring out the GCF:

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

2. Set each factor equal to zero:

   • \( 46x = 0 \) → \( x = 0 \)
   • \( x - 3 = 0 \) → \( x = 3 \)

The solutions are: \[ x = 0 \quad \text{and} \quad x = 3. \]