Ask a New Question
Menu

Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x^2 = 56x

1 answer

To factor out the greatest common factor (GCF) and solve the quadratic equation \( 7x^2 = 56x \), we can follow these steps:

  1. Set the equation to zero: First, we want to bring all terms to one side of the equation to set it to zero: \[ 7x^2 - 56x = 0 \]

  2. Find the GCF: The GCF of the terms \( 7x^2 \) and \( -56x \) is \( 7x \).

  3. Factor out the GCF: \[ 7x(x - 8) = 0 \]

  4. Set each factor to zero: According to the zero product property, if the product is zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero: \[ 7x = 0 \quad \text{or} \quad x - 8 = 0 \]

  5. Solve each equation:

    • From \( 7x = 0 \): \[ x = 0 \]
    • From \( x - 8 = 0 \): \[ x = 8 \]

  6. Final solutions: The solutions to the equation are: \[ x = 0 \quad \text{or} \quad x = 8 \]

In summary, the steps to factor and solve the equation \( 7x^2 = 56x \) are:

  • Set equation to zero: \( 7x^2 - 56x = 0 \)
  • Factor out the GCF: \( 7x(x - 8) = 0 \)
  • Solve for \( x \): \( x = 0 \) or \( x = 8 \)

If you have the specific tables you would like to compare, please provide them, and I can help you determine which one shows these steps correctly.