To solve the quadratic equation \( 2x^2 - 14x = 0 \) by factoring out the greatest common factor (GCF), we start by identifying the GCF of the terms 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:
- \( 2x = 0 \)
- \( x - 7 = 0 \)
From the first equation:
\[ 2x = 0 \implies x = 0 \]
From the second equation:
\[ x - 7 = 0 \implies x = 7 \]
Thus, the solutions to the equation are:
- The smaller solution is \( x = 0 \)
- The larger solution is \( x = 7 \)
In summary:
The smaller solution is \( x = 0 \), and the larger solution is \( x = 7 \).