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

Question

a x = -3
b x = -3, x = 3
c x = 9, x = -9
d x = 3

Answer 1

To solve the equation \( 3x^2 - 20 = 7 \), we first need to simplify it:

1. Start by adding 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: \[ x^2 = \frac{27}{3} = 9 \]

3. Now, take the square root of both sides. Remember that we take both the positive and negative roots: \[ x = \sqrt{9} \quad \text{or} \quad x = -\sqrt{9} \] This gives us: \[ x = 3 \quad \text{or} \quad x = -3 \]

Thus, the solutions are \( x = 3 \) and \( x = -3 \).

The correct answer from the options provided is: b) x = -3, x = 3.