Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x^2 − 14x = 0.

Question

The smaller solution is x =
The large solution is x =

Answer 1

To solve the quadratic equation \( 2x^2 - 14x = 0 \) by factoring out the greatest common factor (GCF), follow these steps:

1. Identify the GCF: The GCF of the terms \( 2x^2 \) and \( -14x \) is \( 2x \).

2. Factor the GCF out of the equation: \[ 2x(x - 7) = 0 \]

3. Set each factor to zero:

   • First factor: \( 2x = 0 \)
   • Second factor: \( x - 7 = 0 \)

4. Solve for \( x \):

   • From \( 2x = 0 \): \[ x = 0 \]
   • From \( x - 7 = 0 \): \[ x = 7 \]

Thus, the solutions to the equation are:

• The smaller solution is \( x = 0 \).
• The larger solution is \( x = 7 \).