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=9 , x=−9 x equals 9 , x equals negative 9 x=3 x equals 3 x=−3 x equals negative 3

Answer 1

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

\[ 3x^2 - 20 - 7 = 0 \]

This simplifies to:

\[ 3x^2 - 27 = 0 \]

Next, we can factor out the common term:

\[ 3(x^2 - 9) = 0 \]

Now we can recognize that \(x^2 - 9\) is a difference of squares, which can be factored further:

\[ 3(x - 3)(x + 3) = 0 \]

Setting each factor equal to zero gives us the solutions:

1. \(x - 3 = 0 \Rightarrow x = 3\)
2. \(x + 3 = 0 \Rightarrow x = -3\)

Thus, the solutions to the equation are:

\[ x = 3 \quad \text{and} \quad x = -3 \]

Among the provided responses, the correct answers are:

• \(x = 3, x = -3\)
• \(x \text{ equals } 3, x \text{ equals } -3\)

So either of those representations of the solution is correct.