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 in the equation.
The GCF of \(2x^2\) and \(-14x\) is \(2x\). We factor \(2x\) out of the equation:
\[ 2x(x - 7) = 0 \]
Next, we set each factor equal to zero:
- \(2x = 0\)
- \(x - 7 = 0\)
From the first equation, we solve for \(x\): \[ x = 0 \]
From the second equation, we solve for \(x\): \[ x = 7 \]
Thus, the solutions to the quadratic equation \(2x^2 - 14x = 0\) are:
- The smaller solution is \(x = 0\).
- The larger solution is \(x = 7\).
Final answer:
- The smaller solution is \(x = 0\).
- The larger solution is \(x = 7\).