gwen was asked to solve 3x^2-20=7 by factoring using the difference of squares pattern. what is/are the correct solution(s). x=-3,x=3. x=-3, x=9,x=-9. x=3

Answer 1

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

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

This simplifies to:

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

Now, we can factor out a common factor from the left side:

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

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

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

Now, we set each factor equal to zero:

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

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

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

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