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)

Answer 1

To solve the equation \(3x^2 - 20 = 7\) by factoring, we first need to rearrange the equation:

1. **Move all terms to one side:**
\[
3x^2 - 20 - 7 = 0
\]
\[
3x^2 - 27 = 0
\]

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

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

4. **Thus, we have:**
\[
3(x - 3)(x + 3) = 0
\]

5. **Set each factor equal to zero:**
\[
3 = 0 \quad \text{(not applicable)}
\]
\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]

So, the solutions to the equation \(3x^2 - 20 = 7\) are \(x = 3\) and \(x = -3\).

Thus, the correct solutions are:
\[
\boxed{3 \text{ and } -3}
\]