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Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 722 = 56x? Put the quadratic in standard form 7x ^ 2 + 56x = 0 Factor out the GCF 7x(x+8)=0 Set each factor equal to zero 720 andx+8=0 The solutions are x = - 8an * dx = 0 Put the quadratic in standard form x - 8 = 0 No GCF Factor out the GCF Set each factor equal to zero r - 8 = 0 The solutions are 1=8 Put the quadratic in standard form 7x ^ 2 - 56x = 0 Factor out the GCF 7x(x - 8) = 0 720 and z-8-0 Set each factor equal to zero The solutions are = - 7an * dx = 8 Factor out the GCF Put the quadratic in standard form 7z2560 7x(x - 8) = 0; x= 0and x^ ** Set each factor equal to zero The solutions are 0 and z 8

1 answer

Let's analyze the information provided and correct the steps to factor out the Greatest Common Factor (GCF) and solve the quadratic equation \( 722 = 56x \).

  1. Put the quadratic in standard form: The original equation is \( 722 = 56x \). Rearranging this to standard form (0 on one side) gives: \[ 56x - 722 = 0 \] To put it in standard quadratic form \( 7x^2 + 56x = 0 \), we must first clarify the equation. It seems you intended to write \( 7x^2 + 56x = 0 \) with a GCF of 7 factored out from a related equation. We have: \[ 7x^2 + 56x = 0 \]

  2. Factor out the GCF: The GCF of \( 7x^2 \) and \( 56x \) is \( 7x \): \[ 7x(x + 8) = 0 \]

  3. Set each factor equal to zero: From the factored form \( 7x(x + 8) = 0 \), set each factor equal to zero: \[ 7x = 0 \quad \text{and} \quad x + 8 = 0 \]

  4. Solve for \( x \):

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

Final Solutions: The solutions are \( x = 0 \) and \( x = -8 \).

Correct Steps:

  1. Put the quadratic in standard form: \( 7x^2 + 56x = 0 \)
  2. Factor out the GCF: \( 7x(x + 8) = 0 \)
  3. Set each factor equal to zero: \( 7x = 0 \) and \( x + 8 = 0 \)
  4. Solutions are \( x = 0 \) and \( x = -8 \).

Please note that there are errors in the options you provided, such as "7x2560" (which seems nonsensical) and other typographical errors. This detailed explanation shows the correct procedure to factor and solve the quadratic equation you mentioned.