Question
Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=0
.(1 point)
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GPT-4o mini
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 \( 2x \). Thus, we can factor \( 2x \) out of the equation:
\[
2x(x - 7) = 0
\]
Next, we set each factor equal to zero:
1. \( 2x = 0 \)
2. \( x - 7 = 0 \)
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 \( 2x^2 - 14x = 0 \) are:
\[
\boxed{0} \quad \text{and} \quad \boxed{7}
\]
The GCF of \( 2x^2 \) and \( -14x \) is \( 2x \). Thus, we can factor \( 2x \) out of the equation:
\[
2x(x - 7) = 0
\]
Next, we set each factor equal to zero:
1. \( 2x = 0 \)
2. \( x - 7 = 0 \)
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 \( 2x^2 - 14x = 0 \) are:
\[
\boxed{0} \quad \text{and} \quad \boxed{7}
\]
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