Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=0.(1 point)

Question

The smaller solution is x=
, and the larger solution is x=
.
Remaining Attempts : 3

Answer 1

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

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

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

3. Set each factor to zero:

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

4. Solutions:

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

Thus, the final answers are:

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