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 terms are \(2x^2\) and \(-14x\). The GCF of these terms is \(2x\).
Now, we factor out \(2x\) from the equation:
\[ 2x(x - 7) = 0 \]
Next, we set each factor equal to zero:
- \(2x = 0\)
- \(x - 7 = 0\)
Solving these equations gives us:
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From \(2x = 0\): \[ x = 0 \]
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From \(x - 7 = 0\): \[ x = 7 \]
Thus, the solutions to the equation \(2x^2 - 14x = 0\) are:
\[ \boxed{0} \quad \text{and} \quad \boxed{7} \]
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