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 \(2x\). Now we factor \(2x\) out of the equation:
\[ 2x(x - 7) = 0 \]
Next, we set each factor equal to zero:
- \(2x = 0\)
- \(x - 7 = 0\)
For the first equation:
\[ 2x = 0 \implies x = 0 \]
For the second equation:
\[ x - 7 = 0 \implies x = 7 \]
Thus, the solutions are \(x = 0\) and \(x = 7\).
The smaller solution is \(x = 0\) and the larger solution is \(x = 7\).
Final answers:
- Smaller solution: \(x = 0\)
- Larger solution: \(x = 7\)
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