Question
Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x^2=56x
Answers
GPT-4o mini
To factor out the greatest common factor (GCF) and solve the quadratic equation \(7x^2 = 56x\), we can follow these steps:
1. **Set the equation to zero**: We want all terms on one side of the equation.
\[
7x^2 - 56x = 0
\]
2. **Factor the left-hand side**: Identify the GCF of the terms.
- The GCF of \(7x^2\) and \(56x\) is \(7x\).
- Factor out \(7x\):
\[
7x(x - 8) = 0
\]
3. **Use the Zero Product Property**: Set each factor equal to zero.
- \(7x = 0\) or \(x - 8 = 0\)
4. **Solve each equation**:
- From \(7x = 0\):
\[
x = 0
\]
- From \(x - 8 = 0\):
\[
x = 8
\]
5. **Write down the final solution**: The solutions to the equation \(7x^2 = 56x\) are:
\[
x = 0 \quad \text{or} \quad x = 8
\]
In summary, to solve the quadratic equation \(7x^2 = 56x\), we factor out the GCF \(7x\), set each factor to zero, and solve to find the solutions \(x = 0\) and \(x = 8\).
1. **Set the equation to zero**: We want all terms on one side of the equation.
\[
7x^2 - 56x = 0
\]
2. **Factor the left-hand side**: Identify the GCF of the terms.
- The GCF of \(7x^2\) and \(56x\) is \(7x\).
- Factor out \(7x\):
\[
7x(x - 8) = 0
\]
3. **Use the Zero Product Property**: Set each factor equal to zero.
- \(7x = 0\) or \(x - 8 = 0\)
4. **Solve each equation**:
- From \(7x = 0\):
\[
x = 0
\]
- From \(x - 8 = 0\):
\[
x = 8
\]
5. **Write down the final solution**: The solutions to the equation \(7x^2 = 56x\) are:
\[
x = 0 \quad \text{or} \quad x = 8
\]
In summary, to solve the quadratic equation \(7x^2 = 56x\), we factor out the GCF \(7x\), set each factor to zero, and solve to find the solutions \(x = 0\) and \(x = 8\).