To solve the equation \(3x^2 - 20 = 7\) by factoring using the difference of squares pattern, 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 factor of 3:
\[3(x^2 - 9) = 0\]
Now we 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:
- \(x - 3 = 0\) → \(x = 3\)
- \(x + 3 = 0\) → \(x = -3\)
Thus, the solutions to the equation \(3x^2 - 20 = 7\) are:
\[x = 3 \quad \text{and} \quad x = -3\]
So the correct response is:
x = −3, x = 3 (x equals negative 3, x equals 3).