Question

Gwen was asked to solve 3x^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 equals 3 x=3 x equals 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, we first need to rearrange it into a standard form.

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

2. Next, we can factor out the common term. We can first factor out a \(3\):
\[
3(x^2 - 9) = 0
\]

3. Recognizing \(x^2 - 9\) as a difference of squares, we can factor it further:
\[
3(x - 3)(x + 3) = 0
\]

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

Thus, the solutions to the equation are \(x = 3\) and \(x = -3\).

Based on the provided responses, the correct answers are:
- \(x = -3, x = 3\)
- \(x = 3, x = -3\)

Both responses indicate the same solutions.