Question

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

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 equal to zero**:
\[
2x = 0 \quad \text{or} \quad x - 7 = 0
\]

4. **Solve for \( x \)**:
- From \( 2x = 0 \):
\[
x = 0
\]
- From \( x - 7 = 0 \):
\[
x = 7
\]

Thus, the solutions are:
- The smaller solution is \( x = 0 \).
- The larger solution is \( x = 7 \).

Final answers:
- The smaller solution is \( x = 0 \), and the larger solution is \( x = 7 \).