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

Question

Responses

x=−3
x is equal to negative 3

x=−3, x=3
x=−3, x=3

x=9, x=−9
x=9, x=−9

x=3

Answer 1

To solve the equation \(3x^2 - 20 = 7\), let's first rearrange it:

1. Add 20 to both sides of the equation: \[ 3x^2 - 20 + 20 = 7 + 20 \] This simplifies to: \[ 3x^2 = 27 \]

2. Next, divide both sides by 3: \[ x^2 = 9 \]

3. Now, take the square root of both sides: \[ x = 3 \quad \text{or} \quad x = -3 \]

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

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

Thus, the correct response is:

x=−3, x=3 (x=−3, x=3).