To solve the quadratic equation \(2x^2 - 14x = 0\) by factoring out the greatest common factor (GCF), we first identify the GCF in the equation.
The GCF of \(2x^2\) and \(-14x\) is \(2x\).
Now, we factor \(2x\) out of the equation:
\[ 2x(x - 7) = 0 \]
Now, we can set each factor equal to zero:
- \(2x = 0\)
- \(x - 7 = 0\)
For the first equation \(2x = 0\):
\[ x = 0 \]
For the second equation \(x - 7 = 0\):
\[ x = 7 \]
Thus, the solutions to the equation are \(x = 0\) and \(x = 7\).
The smaller solution is \(x = 0\), and the larger solution is \(x = 7\).