Gwen was asked to solve 3x2−20=7

Question

3
𝑥
2
−
20
=
7
by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses

x=−3
𝑥
=
−
3
x equals negative 3

x=9
𝑥
=
9
, x=−9
𝑥
=
−
9
x equals 9 , x equals negative 9

x=−3
𝑥
=
−
3
, x=3
𝑥
=
3
x equals negative 3 , x equals 3

x=3

Answer 1

To solve the equation \(3x^2 - 20 = 7\) using the difference of squares pattern, we first need to rearrange the equation to set it to zero.

1. Start with the given equation: \[ 3x^2 - 20 = 7 \]

2. Subtract 7 from both sides: \[ 3x^2 - 20 - 7 = 0 \] \[ 3x^2 - 27 = 0 \]

3. Factor out the common term: \[ 3(x^2 - 9) = 0 \]

4. Now, we can see that \(x^2 - 9\) is a difference of squares, and it can be factored further: \[ 3(x - 3)(x + 3) = 0 \]

5. Set each factor equal to zero:

   1. \(x - 3 = 0 \rightarrow x = 3\)
   2. \(x + 3 = 0 \rightarrow x = -3\)

Thus, the solutions to the equation \(3x^2 - 20 = 7\) are: \[ x = 3 \quad \text{and} \quad x = -3 \]

The correct response is:

• \(x = -3\), \(x = 3\) (x equals negative 3, x equals 3).