Question

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