Question
solve the following quadratic equation by factoring out the greatest common factor (GCF): 2 x 2−14x=0 .(1 point) The smaller solution is x= , and the larger solution is x= .
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GPT 3.5
To solve the quadratic equation by factoring out the greatest common factor (GCF), we first identify the GCF of the terms.
The two terms in the equation are 2x² and -14x. The GCF of these terms is 2x.
Next, we divide both terms by the GCF (2x) to factor it out:
(2x)(x - 7) = 0
Then, we set each factor equal to zero and solve for x:
2x = 0 → x = 0
x - 7 = 0 → x = 7
Therefore, the smaller solution is x = 0 and the larger solution is x = 7.
The two terms in the equation are 2x² and -14x. The GCF of these terms is 2x.
Next, we divide both terms by the GCF (2x) to factor it out:
(2x)(x - 7) = 0
Then, we set each factor equal to zero and solve for x:
2x = 0 → x = 0
x - 7 = 0 → x = 7
Therefore, the smaller solution is x = 0 and the larger solution is x = 7.
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