Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x

Question

7
𝑥
2
=
56
𝑥
?(1 point)
Responses

Put the quadratic in standard form x−8=0
𝑥
−
8
=
0
Factor out the GCF No GCF
Set each factor equal to zero x−8=0
𝑥
−
8
=
0
The solutions are x=8
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
7
𝑥
2
+
56
𝑥
=
0
Factor out the GCF 7x(x+8)=0
7
𝑥
(
𝑥
+
8
)
=
0
Set each factor equal to zero 7x=0
7
𝑥
=
0
and x+8=0
𝑥
+
8
=
0
The solutions are x=−8
𝑥
=
−
8
and x=0
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 equal

Answer 1

To solve the quadratic equation \( 7x^2 = 56x \), we first need to rearrange it into standard form \( 7x^2 - 56x = 0 \).

Next, we can factor out the GCF (greatest common factor) from the equation. The GCF in this case is \( 7x \):

\[ 7x(x - 8) = 0 \]

Now, we set each factor equal to zero:

1. \( 7x = 0 \)
2. \( x - 8 = 0 \)

Solving these equations gives us:

1. From \( 7x = 0 \), we get \( x = 0 \).
2. From \( x - 8 = 0 \), we get \( x = 8 \).

Thus, the solutions are \( x = 0 \) and \( x = 8 \).

The correct table of steps is as follows:

• 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 \( x = 8 \)

From the provided options, the correct response that reflects these steps is this one:

Put the quadratic in standard form: \( 7x^2 + 56x = 0 \) (should be \( 7x^2 - 56x = 0 \))
Factor out the GCF: \( 7x(x-8)=0 \)
Set each factor equal to zero: \( 7x=0 \) and \( x + 8=0 \) (this one has a typo, should be \( x - 8 = 0 \))
The solutions are: \( x = -8 \) (this is incorrect, should be \( x = 8 \)) and \( x = 0 \)

Please make sure to note that the representation had errors in the original options and clarify them when selecting. If only one option was correct and complete without errors, select that. If this option had typos (as noted), it might not be fully correct.