Gwen was asked to solve the equation 3x2−20=7

Question

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