Gwen was asked to solve 3x2−20=7

Question

by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses

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

x=3
x equals 3

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

x=−3

Answer 1

To solve the equation \( 3x^2 - 20 = 7 \) by factoring, let's first rearrange it into standard form:

1. Move 7 to the left side: \[ 3x^2 - 20 - 7 = 0 \] This simplifies to: \[ 3x^2 - 27 = 0 \]

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

3. Identify the difference of squares: \[ x^2 - 9 = (x - 3)(x + 3) \] Therefore, we have: \[ 3(x - 3)(x + 3) = 0 \]

4. Set each factor equal to zero: \[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \] \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \]

The solutions are:

• \( x = 3 \)
• \( x = -3 \)

In summary, the correct response is: x equals 3, x equals negative 3.