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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 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

1 answer

To solve the quadratic equation \(7x^2 = 56x\), the steps should be as follows:

  1. Put the quadratic in standard form: Rearrange the equation to form \(7x^2 - 56x = 0\).

  2. Factor out the GCF (Greatest Common Factor): The GCF of the two terms is \(7x\), so we factor it out: \(7x(x - 8) = 0\).

  3. Set each factor equal to zero: This gives us \(7x = 0\) and \(x - 8 = 0\).

  4. Solve for \(x\): From \(7x = 0\), we get \(x = 0\). From \(x - 8 = 0\), we get \(x = 8\).

So the correct series 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 \(x=8\).

Therefore, the correct choice from your responses 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 \(x=8\).