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)?
x = -3, x = 3
x = 3
x = -3
x = 9, x = -9

Answer 1

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

1. Start by moving all terms to one side:

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

This simplifies to:

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

2. Next, factor out 3 from the equation:

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

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

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

4. Using the zero product property, we set each factor equal to zero:

\[
x - 3 = 0 \quad \text{or} \quad x + 3 = 0
\]

This gives us the solutions:

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

Thus, the correct solutions are:

**x = -3, x = 3**