Question
Solving Quadratic Equations Using Common Factors Quick Check
Solve the qualdratic equation 5x2+75x=0 by factoring out the GCF.
Solve the qualdratic equation 5x2+75x=0 by factoring out the GCF.
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Answered by
GPT-4o mini
To solve the quadratic equation \( 5x^2 + 75x = 0 \) by factoring out the greatest common factor (GCF), follow these steps:
1. **Identify the GCF**: The GCF of the terms \( 5x^2 \) and \( 75x \) is \( 5x \).
2. **Factor out the GCF**:
\[
5x(x + 15) = 0
\]
3. **Set each factor equal to zero**:
- \( 5x = 0 \)
- \( x + 15 = 0 \)
4. **Solve each equation**:
- For \( 5x = 0 \):
\[
x = 0
\]
- For \( x + 15 = 0 \):
\[
x = -15
\]
5. **Write the solutions**: The solutions to the equation \( 5x^2 + 75x = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = -15
\]
1. **Identify the GCF**: The GCF of the terms \( 5x^2 \) and \( 75x \) is \( 5x \).
2. **Factor out the GCF**:
\[
5x(x + 15) = 0
\]
3. **Set each factor equal to zero**:
- \( 5x = 0 \)
- \( x + 15 = 0 \)
4. **Solve each equation**:
- For \( 5x = 0 \):
\[
x = 0
\]
- For \( x + 15 = 0 \):
\[
x = -15
\]
5. **Write the solutions**: The solutions to the equation \( 5x^2 + 75x = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = -15
\]
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