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)? (1 point)
$x=9,x=-9$
$x=3$
$x=-3,x=3$
$x=-3$

Answer 1

To solve the equation \(3x^{2} - 20 = 7\), we first rearrange it:

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

This simplifies to:

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

Next, we can factor out a common term:

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

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

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

Setting each factor equal to zero gives us the possible solutions:

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

Thus, the solutions are:

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

The correct answer is:

\[
x = -3, x = 3
\]