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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 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=−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 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 rearrange it into standard form.

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

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

  3. Set each factor equal to zero:

    • First factor: \( 7x = 0 \) → \( x = 0 \)
    • Second factor: \( x - 8 = 0 \) → \( x = 8 \)

The solutions to the equation are:

  • \( x = 0 \)
  • \( x = 8 \)

Looking at the responses you provided, the correct table is:

Response: 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 response clearly outlines the steps correctly and provides the accurate solutions.