Question

Gwen was asked to solve the equation 3x2−20=7
3
x
2
−
20
=
7
. What is/are the correct solution(s)?(1 point)
Responses

x=−3
x
=
−
3
x is equal to negative 3

x=−3, x=3
x
=
−
3
,

x
=
3
x=−3, x=3
x
=
−
3
,

x
=
3

x=9, x=−9
x
=
9
,

x
=
−
9
x=9, x=−9
x
=
9
,

x
=
−
9

x=3

Answer 1

To solve the equation \( 3x^2 - 20 = 7 \), we can follow these steps:

1. **Add 20 to both sides**:
\[
3x^2 - 20 + 20 = 7 + 20
\]
\[
3x^2 = 27
\]

2. **Divide both sides by 3**:
\[
\frac{3x^2}{3} = \frac{27}{3}
\]
\[
x^2 = 9
\]

3. **Take the square root of both sides**:
\[
x = \pm 3
\]

Thus, the solutions to the equation are:
\[
x = -3 \quad \text{and} \quad x = 3
\]

The correct answer is:
**x = −3, x = 3**