Question
Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x^2−14x=0
.(1 point)
The smaller solution is x=
, and the larger solution is x=
.
.(1 point)
The smaller solution is x=
, and the larger solution is x=
.
Answers
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Answered by
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 on the left side.
The GCF of \( 2x^2 \) and \( -14x \) is \( 2x \). We can factor this out:
\[
2x(x - 7) = 0
\]
Now we have a product equal to zero, which means that we can set each factor equal to zero:
1. \( 2x = 0 \)
2. \( x - 7 = 0 \)
Solving the first equation:
\[
2x = 0 \implies x = 0
\]
Solving the second equation:
\[
x - 7 = 0 \implies x = 7
\]
So the solutions to the equation \( 2x^2 - 14x = 0 \) are \( x = 0 \) and \( x = 7 \).
Thus, the smaller solution is \( x = 0 \), and the larger solution is \( x = 7 \).
The GCF of \( 2x^2 \) and \( -14x \) is \( 2x \). We can factor this out:
\[
2x(x - 7) = 0
\]
Now we have a product equal to zero, which means that we can set each factor equal to zero:
1. \( 2x = 0 \)
2. \( x - 7 = 0 \)
Solving the first equation:
\[
2x = 0 \implies x = 0
\]
Solving the second equation:
\[
x - 7 = 0 \implies x = 7
\]
So the solutions to the equation \( 2x^2 - 14x = 0 \) are \( x = 0 \) and \( x = 7 \).
Thus, the smaller solution is \( x = 0 \), and the larger solution is \( x = 7 \).
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