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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 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

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

1 answer

To solve the quadratic equation \(7x^2 = 56x\), we first need to move all the terms to one side to put it in standard form:

  1. Rearranging gives:
    \[ 7x^2 - 56x = 0 \]

  2. Next, we factor out the greatest common factor (GCF) which is \(7x\):
    \[ 7x(x - 8) = 0 \]

  3. Then, we set each factor equal to zero: \[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]

  4. Solving these equations gives:

    • From \(7x = 0\), we get \(x = 0\)
    • From \(x - 8 = 0\), we get \(x = 8\)

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

The correct response from the provided options 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 \(x = 8\)

This corresponds to the third option in your list.