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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=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=−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=−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

1 answer

To solve the quadratic equation \(7x^2 = 56x\), we first need to transform it into standard form by moving all terms to one side.

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

  2. Factor out the GCF: The greatest common factor (GCF) is \(7x\). \[ 7x(x - 8) = 0 \]

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

  4. Solve for \(x\):

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

Thus, the solutions are: \[ x = 0 \quad \text{and} \quad x = 8 \]

The correct response includes:

  • Putting the quadratic in standard form as \(7x^2 - 56x = 0\),
  • Factoring out the GCF to get \(7x(x - 8) = 0\),
  • Setting each factor equal to zero,
  • Concluding the solutions are \(x = 0\) and \(x = 8\).

The choice that matches this description is the second option:

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 \(x = 8\)