To solve the quadratic equation \( 2x^2 - 14x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms on the left side.
The GCF of \( 2x^2 \) and \( -14x \) is \( 2x \). We can factor this out:
\[ 2x(x - 7) = 0 \]
Now we have a product equal to zero, which means that we can set each factor equal to zero:
- \( 2x = 0 \)
- \( x - 7 = 0 \)
Solving the first equation:
\[ 2x = 0 \implies x = 0 \]
Solving the second equation:
\[ x - 7 = 0 \implies x = 7 \]
So the solutions to the equation \( 2x^2 - 14x = 0 \) are \( x = 0 \) and \( x = 7 \).
Thus, the smaller solution is \( x = 0 \), and the larger solution is \( x = 7 \).