Question

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

Answer 1

To solve the equation \( 3x^2 - 20 = 7 \), we first want to isolate the \( x^2 \) term.

1. Start by adding 20 to both sides of the equation:
\[
3x^2 - 20 + 20 = 7 + 20
\]
Which simplifies to:
\[
3x^2 = 27
\]

2. Next, divide both sides by 3 to solve for \( x^2 \):
\[
x^2 = \frac{27}{3}
\]
This simplifies to:
\[
x^2 = 9
\]

3. Now, take the square root of both sides:
\[
x = \pm \sqrt{9}
\]
Which gives:
\[
x = \pm 3
\]

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

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