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 \( 2x^2 \) and \( -14x \). The GCF is \( 2x \).
Now, we can factor out \( 2x \) from the equation:
\[ 2x(x - 7) = 0 \]
Next, we set each factor equal to zero to find the solutions:
- \( 2x = 0 \)
- \( x - 7 = 0 \)
From the first factor:
\[ 2x = 0 \implies x = 0 \]
From the second factor:
\[ x - 7 = 0 \implies x = 7 \]
Thus, the solutions to the equation are \( x = 0 \) and \( x = 7 \).
The smaller solution is \( x = 0 \), and the larger solution is \( x = 7 \).
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