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: \[ \boxed{3 \text{ and } -3} \]