Question

Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x?(1 point)ResponsesPut the quadratic in standard formx−8=0Factor out the GCFNo GCFSet each factor equal to zerox−8=0The solutions arex=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 8Put the quadratic in standard form7x2−56x=0Factor out the GCF7x(x−8)=0Set each factor equal to zero7x=0 and x−8=0The solutions arex=0 and x=8Put 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 8Put the quadratic in standard form7x2−56x=0Factor out the GCF7x(x−8)=0Set each factor equal to zero7x=0 and x−8=0The solutions arex=−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 8Put the quadratic in standard form7x2+56x=0Factor out the GCF7x(x+8)=0Set each factor equal to zero7x=0 and x+8=0The solutions arex=−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 0Skip to navigation

Answer 1

To solve the quadratic equation \( 7x^2 = 56x \), we first need to rearrange it into standard form:

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

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

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

4. **Solve for \( x \)**:
\[
x = 0 \quad \text{and} \quad x = 8
\]

Therefore, the correct sequence of steps 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 \( x = 8 \)

The option that matches these steps in the response list 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 \( x = 8 \)**.