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 $x=$
$(GCF)$
$2x^{2}-14x=0$
(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 in the equation.
The GCF of \(2x^2\) and \(-14x\) is \(2x\). We can factor \(2x\) out from the equation:
\[
2x(x - 7) = 0
\]
Next, we set each factor equal to zero to find the solutions:
1. Setting the first factor equal to zero:
\[
2x = 0 \implies x = 0
\]
2. Setting the second factor equal to zero:
\[
x - 7 = 0 \implies x = 7
\]
Thus, the solutions to the equation are:
- The smaller solution is \(x = 0\).
- The larger solution is \(x = 7\).
In summary, the answers are:
- The smaller solution is \(x = 0\)
- The larger solution is \(x = 7\)
The GCF of \(2x^2\) and \(-14x\) is \(2x\). We can factor \(2x\) out from the equation:
\[
2x(x - 7) = 0
\]
Next, we set each factor equal to zero to find the solutions:
1. Setting the first factor equal to zero:
\[
2x = 0 \implies x = 0
\]
2. Setting the second factor equal to zero:
\[
x - 7 = 0 \implies x = 7
\]
Thus, the solutions to the equation are:
- The smaller solution is \(x = 0\).
- The larger solution is \(x = 7\).
In summary, the answers are:
- The smaller solution is \(x = 0\)
- The larger solution is \(x = 7\)
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