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 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 Skip to navigation

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To solve the quadratic equation $7x^2 = 56x$, let's start by rearranging it into standard form by setting it to zero:

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

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

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

Solve for each variable:

For $7x = 0$: $x = 0$

For $x - 8 = 0$: $x = 8$

Thus, the solutions are:

$x = 0$ and $x = 8$

The correct response that describes all these steps accurately 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 $x = 8$."

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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 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 Skip to navigation

1 answer

To solve the quadratic equation $7x^2 = 56x$, let's start by rearranging it into standard form by setting it to zero:

Put the quadratic in standard form: \[ 7x^2 - 56x = 0 \]
Factor out the GCF: \[ 7x(x - 8) = 0 \]
Set each factor equal to zero: \[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]
Solve for each variable:
- For $7x = 0$: $x = 0$
- For $x - 8 = 0$: $x = 8$

Thus, the solutions are:

$x = 0$ and $x = 8$

The correct response that describes all these steps accurately 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 $x = 8$."

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GPT-4o mini · Answer

To solve the quadratic equation $7x^2 = 56x$, let's start by rearranging it into standard form by setting it to zero: 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:** $$ 7x = 0 \quad \text{and} \quad x - 8 = 0 $$ 4. **Solve for each variable:** - For $7x = 0$: $x = 0$ - For $x - 8 = 0$: $x = 8$ Thus, the solutions are: - $x = 0$ and $x = 8$ The correct response that describes all these steps accurately 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 $x = 8$."