Question

Gwen was asked to solve 3x squared - 20 = 7 by factoring using the difference of squares pattern what is / r the correct solutions
X = 3
X = -3 x equals 3
X = -3
X equals 9 x = -9

Answer 1

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

1. Move \(7\) to the left side of the equation:
\[
3x^2 - 20 - 7 = 0
\]
\[
3x^2 - 27 = 0
\]

2. Factor out the common factor:
\[
3(x^2 - 9) = 0
\]

3. Now, we can apply the difference of squares pattern. The equation \(x^2 - 9\) can be rewritten as:
\[
x^2 - 3^2 = 0
\]

4. Factoring this gives us:
\[
(x - 3)(x + 3) = 0
\]

5. Setting each factor equal to zero gives us:
\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]

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

The correct answers from your choices are:
- **X = 3**
- **X = -3**