Question

Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x ?(1 point) Responses Put the quadratic in standard form x−8=0 Factor out the GCF No GCF Set each factor equal to zero x−8=0 The solutions are x=8 Put the quadratic in standard form x minus 8 equals 0 Factor out the GCF No GCF Set each factor equal to zero x minus 8 equals 0 The solutions are x equals 8 Put the quadratic in standard form 7x2−56x=0 Factor out the GCF 7x(x−8)=0 Set each factor equal to zero 7x=0 and x−8=0 The solutions are x=0 and x=8 Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals 0 and x equals 8 Put the quadratic in standard form 7x2+56x=0 Factor out the GCF 7x(x+8)=0 Set each factor equal to zero 7x=0 and x+8=0 The solutions are x=−8 and x=0 Put the quadratic in standard form 7 x squared plus 56 x equals 0 Factor out the GCF 7 x left parenthesis x plus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x plus 8 equals 0 The solutions are x equals negative 8 and x equals 0 Put the quadratic in standard form 7x2−56x=0 Factor out the GCF 7x(x−8)=0 Set each factor equal to zero 7x=0 and x−8=0 The solutions are x=−7 and x=8 Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals negative 7 and x equals 8 Skip to navigation

Answer 1

To solve the quadratic equation \(7x^2 = 56x\), let's start by rearranging it into standard form by setting it to zero:

1. **Put the quadratic in standard form:**
\[
7x^2 - 56x = 0
\]

2. **Factor out the GCF:**
\[
7x(x - 8) = 0
\]

3. **Set each factor equal to zero:**
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]

4. **Solve for each variable:**
- For \(7x = 0\): \(x = 0\)
- For \(x - 8 = 0\): \(x = 8\)

Thus, the solutions are:
- \(x = 0\) and \(x = 8\)

The correct response that describes all these steps accurately is:
"Put the quadratic in standard form \(7x^2 - 56x = 0\). Factor out the GCF \(7x(x - 8) = 0\). Set each factor equal to zero \(7x = 0\) and \(x - 8 = 0\). The solutions are \(x = 0\) and \(x = 8\)."