Solving Quadratic Equations Using Common Factors Practice

Question

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Question
Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=0
.(1 point)
The smaller solution is x=
, and the larger solution is x=
.
Remaining Attempts : 3
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Answer 1

To solve the quadratic equation \(2x^2 - 14x = 0\) by factoring out the greatest common factor (GCF), we start by finding the GCF of the terms.

1. Identify the GCF: The GCF of \(2x^2\) and \(14x\) is \(2x\).

2. Factor out the GCF: \[ 2x(x - 7) = 0 \]

3. Set each factor equal to zero:

   • \(2x = 0\)
   • \(x - 7 = 0\)

4. Solve each equation:

   • From \(2x = 0\), we get: \[ x = 0 \]
   • From \(x - 7 = 0\), we get: \[ x = 7 \]

5. Conclude the solutions: The smaller solution is \(x = 0\), and the larger solution is \(x = 7\).

So the final answers are:

• The smaller solution is \(x = 0\).
• The larger solution is \(x = 7\).