Question

Solving Quadratic Equations Using Common Factors Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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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 \(x = 7\).