Question

Solve the following quadratic equation by factoring out the greatest common factor (GCF):  2x^2 − 14x = 0.
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 \( x = 7 \).