Question

Gwen was asked to solve 3x2−20=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 equals 3

x=−3
x equals negative 3

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

x=3

Answer 1

To solve the equation \( 3x^2 - 20 = 7 \) by factoring using the difference of squares pattern, we first rewrite the equation:

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

2. Factor the left side:
We can factor this as:
\[
3(x^2 - 9) = 0
\]

3. Recognize that \( x^2 - 9 \) is a difference of squares:
\[
3(x - 3)(x + 3) = 0
\]

4. Set each factor to zero:
\[
3 = 0 \text{ (not applicable)}
\]
\[
x - 3 = 0 \implies x = 3
\]
\[
x + 3 = 0 \implies x = -3
\]

Therefore, the solutions are \( x = -3 \) and \( x = 3 \).

So, the correct responses would be:
- \( x = -3, x = 3 \)
- \( x \text{ equals negative 3, } x \text{ equals } 3 \)

Both of these options represent the same solutions.